In The Party, Kevin throws his husband a birthday party and invites his colleagues at the Nine-Nine, who assume that Kevin invited them because Holt didn't want them there. When they arrive at the party, Kevin is instantly curt and snobby to Holt's colleagues. He also continuously needles Peralta, making him uncomfortable. Later Kevin and Holt start fighting about how Kevin is acting around his guests. Jake, Amy, and Terry are hiding in the bathroom and they learn that Kevin only invited them there because Holt asked him to. Kevin and Holt ask them to leave. Later, Jake realizes why Kevin wouldn't allow cops. Kevin dislikes cops because of the way Holt's former colleagues discriminated against him for his race and sexuality. When Jake plans a private evening for Kevin and Holt, his feelings toward the detective seem to soften, and they even play a small prank on Holt together, in which Kevin asks Jake to call him "Kev," a nickname Holt knows he hates.
In The Mole, Kevin briefly appears, answering the door to his and Holt's house when Jake shows up to find out who the mole is with Holt. Kevin calls out to Holt, stating that his "work-life is here".
In USPIS, Holt answers a call where the phone conversation is about Kevin asking if Holt has seen his belt and accusing the housekeeper of stealing it.
In The Road Trip, Holt wants to do something special for Kevin, for their anniversary. At first, it was learning to cook an omelet but in an upset at how Charles is teaching him, Holt said he is going to make Kevin plain toast for breakfast. The next morning, though, Holt tells Charles that he made Kevin a Croque monsieur. He mentions that Kevin and he shared one on a rainy afternoon in Paris on their first anniversary and that it is one of their most treasured memories.
In Stakeout, Kevin appears when Marcus and Rosa emerge from his bedroom. Kevin conceals a smile at the situation and invites them to come and join them for breakfast but Rosa feels awkward and leaves.
In Payback, Amy got Holt to try some street meat. Holt accepts having a mystery sauce pour a little on his lamb, to which he said he doesn't care for it but at least he tried and what a story it will be for Kevin.
In The Wednesday Incident, Jake and Gina ask for Kevin's help in finding out why Holt has been in a bad mood. Kevin agrees to help and they talk to all the people Raymond would have seen before work such as Diane, his fencing partner, and his fellow painters. However, when they talk to his fencing partner, Kevin finds out that Holt hasn't been there since last Wednesday. He leaves and is upset, as Holt said he had been fencing and he had lied to him. Jake later thinks that Holt was mugged and goes to tell Kevin. However, Holt comes in and reveals that he fought the men off and was "lightly stabbed" as a result. Kevin is annoyed that Holt lied to him and Jake leaves after being reprimanded by Holt. Later, Kevin appears with Holt and gives Gina and Jake some still life paintings of a grey rock that Holt has done as a thank you.
In Boyle-Linetti Wedding, Kevin attends Darlene and Lynn's wedding with his husband. Holt remarks that he might like to have a more public expression of their love, as their wedding was short as they didn't know how long gay marriage would be legal for. Kevin tells him that if they had had a bigger ceremony he never would have heard Holt's efficient/officiant quip and Holt agrees that he regrets nothing.
In AC/DC, Kevin invites Marcus and Rosa to have dinner with them. Upon arrival, Kevin calls Marcus into the kitchen to help him with the food, leaving Rosa and Holt alone. During the dinner, Kevin attempts to converse with Rosa and she keeps her answers short as to avoid becoming too personally acquainted with Holt.
In The Swedes, he leaves for Paris to teach at the Sorbonne for six months. Before he goes, he and Holt ask Charles to take his place in a squash tournament as they have won for the past few years. Later, over video chat, Kevin congratulates them on winning and says that he is looking to forward to winning next year but Holt says they can't as due to Charles's wild behavior, they are banned for life.
In Skyfire Cycle, he and Holt are arguing about the "Monty Hall Problem" which Kevin brought up during their first dinner together in 2 weeks. They tell the problem to Rosa and Amy wherein Holt decides to stay with the original choice while Kevin says the odds one is better if the decision was changed. They continue arguing about the problem. Later on, Rosa concludes that they're arguing because of the night shift and are simply sexually frustrated. By the end of the episode, Holt says the problem is fixed and it turns out, Rosa was right, to Amy's dismay.
In Two Turkeys, he and Holt are in the 99th precinct with an English Walnut pie that they got at the Cottage Inn in Saratoga Springs after their annual drive upstate. They plan to bring it to Kevin's parents' house that night for Thanksgiving. Kevin had said the pie is the finest sweet treat on Earth, even better than a plain scone. Later on however, the pie goes missing, prompting Holt to accuse Rosa, Terry and Charles of stealing it, although it is later revealed that it was actually Kevin who took the pie and threw it out, admitting that he hated the pie and knew that his parents would too, which could result in them treating Holt even worse, and Kevin wanted to protect his husband. When Holt asks why Kevin didn’t just tell him that he hated the pie, Kevin confesses that he loved their trips to Saratoga Springs and didn’t want that to stop, prompting Holt to suggest that they still continue make yearly the trip but just don’t get the pie anymore. Kevin likes this suggestion, and agrees.
In Safe House, he has to be put in protective custody by Holt, due to the threaten of Seamus Murphy. Jake takes it upon himself to stay with Kevin during the months in the safe house. Kevin has to put writing his book on hold, and instead have to endure watching Nicholas Cage movies with Jake. After two months with Murphy still not caught, Holt and Kevin get into a "vicious fight" over letting him visit the library for just two hours, ending with Kevin doubting whether their relationship will last anyhow once this is all over. When Holt and Jake were captured by Murphy, however, he rescues them by driving through a wall, knocking out Murphy's henchman, and throat-punching Murphy himself. Holt and Kevin makeup and Kevin admits that he will actually miss Jake, as well.
In Casecation, Holt has Kevin on the phone while Jake and Amy are having a structured debate. When Holt feels conflicted as a moderator, in part because he's Amy's superior and therefore being unable to be impartial to judging who gets a point for making a good pro-or-con argument statement, he asks Kevin to decide.
When Jake makes another argument statement that has some personal aspect to it, Kevin states he is conflicted in being impartial to moderate, too.
In The Bimbo, Kevin is at the Precinct saying goodbye to his husband. When Holt wishes Kevin to have a productive day and clasp his hand in a handshake, Kevin acknowledges the PDA (Public Display of Affection). Holt said he couldn't help himself, to which Kevin "Hmm" indicating he didn't hate the PDA. Before Kevin does leave, he asks Holt if he may use the bathroom. Holt says yes and thanks to Kevin for asking permission. Kevin thanks Holt back for granting the permission.
In the bathroom, Kevin secretly meets up with Jake so to ask him to help solve how 3 ancient coins were stolen from his Classical department at Columbia. Jake wants to know why Kevin isn't asking Capt. Holt instead. Kevin tells him that Raymond tends to be overprotective when it involves anything with him. While Jake remains still unsure, Kevin does a Nicolas Cage impression, causing Jake to agree to take the case. Capt. Holt enters the bathroom after this moment, asking Kevin about if he wants them to get tickets to a concert. In his attempt to have Holt not notice that Jake is hiding in the bathroom and to get Holt to leave the bathroom, Kevin rushes in answering Holt that any seating in any section in the first tier.
Starting the investigation, Kevin first shows Jake to the classroom where he teaches. Kevin knows that Jake wants to ask about playing with Kevin's laser pointer. While Jake is showing off, they are discovered by Holt.
Holt reveals that he easily found out about Kevin and Jake's secret investigation because he knows Kevin would never sit in any section of a concert. Kevin says he might and that he is flexible. Holt tests Kevin's bluff by slowly inching closer to clicking on a purchase for seat tickets in the center-left section of the concert. Kevin cracks and admits to Holt that Jake is helping him with a burglary at the university and that he asked Jake not to tell Holt.
Holt asks Kevin if this is about Kevin being embarrassed of him, especially during what happened at the Classics Dept.'s holiday party. Kevin clarifies that it wasn't what Holt said but that Dean Wesley Allister pointed out Holt's mistake and Holt lost his mind and caused a kerfuffle.
At the end of the episode, Kevin stands up for Holt when he is criticized by the Dean, saying that he is as smart as any of his fellow professors but chooses to use his intelligence to make the city a better place and that he hopes he can live up to his standard one day.
In Cinco de Mayo, Kevin brings Holt the cummerbund which he controversially won in the last heist. Holt hides the bracelet (the prize) in a chew toy, which Kevin switches while "leaving". Kevin was repulsed at how competitive the heist got at first, but in the end, he reveals that it is fun and may compete in more heists in the future.
In The Good Ones, Kevin was revealed to have separated with Holt in 2020. However, they confessed they still had feelings for each other in The Lake House. After couples therapy, the couple got back together by the end of episode 7.
Kevin is shown to be quite serious and intellectual as he is head of classics at Columbia University. He can also be quite curt and some would view him as snobby, such as his dismissal of the nine-nine, and in particular, Jake. He does later soften to the detectives- even playing a small prank on his husband with Jake. He also shows a softer side around Holt and Gina as he is kind and friendly around them. He is shown to be as fascinated with details as Holt ("I've been reading the most thrilling footnote." - Safe House, 5x12).
Holt is Kevin's husband. The two get along very well and care deeply for one another, such as when Kevin wanted Holt to tell him everything particularly if they were worrying such as Holt being lightly stabbed. Kevin also considers Holt the funny one. For example, even when they were fighting he found Holt's play on words about needling Jake a new suit hilarious and told him to stop being the funny one. Kevin and Holt met while Kevin was writing an article about Holt for the New Yorker and Kevin said that Holt's answer had him in stitches. Holt revealed in The Good Ones that they were separated, but they confessed their continued feelings for each other in The Lake House. Despite a near break-up in Game of Boyles, he and Holt renew their vows in Renewal.
Jake and Kevin have a complicated relationship. Although Kevin doesn't dislike Jake, Kevin is not fond of cops due to the discrimination Holt has been subject to from detectives who looked very similar to Jake. However, the two seem to have a neutral relationship later as the two agree to play a prank on Holt and Kevin gives Jake and Gina paintings. Their relationship improved during Safe House where Kevin started referring to Jake by name and not by rank. Also during The Bimbo, Kevin appeared to start to like Jake coming to him for help giving him a tour of the university and letting him play with his laser pointer. however, Kevin also thinks that Jake is extremely juvenile, serving him soft drinks whilst others get wine.
Whilst Kevin's relationship with the detectives remains distant, he does become on a first-name basis with Gina. Jake and Gina help Kevin figure out that Holt was mugged on the way to work one morning. Gina and Kevin appear to be on good terms as he is willing to accept her advice even if he rejects the same advice from Jake.
Kevin is close with his husband's nephew, who stayed with them while he was staying in New York City. Kevin tried to learn more about Marcus's girlfriend, Rosa, when she came over for dinner.
- The name Kevin "Cozner" is very similar to actor Kevin Costner. Costner is well-known for his role in Dances with Wolves, which is why Jake asks whether Kevin is the star of "Danzez with Wolvez".
- His brother is the best oral surgeon in the quint state area.
- In The Swedes, he leaves for Paris to teach at the Sorbonne for six months.
- Holt claims that his watch in the Halloween episode of Season Two is a gift from Kevin's father just before he died and thus holds a great deal of sentimental value. As this information was stated in the wider context of a bet there is a chance that it is false. There is further evidence for this being false information in the episode "Mr. Santiago". Holt admits that he was very arrogant when meeting Kevin's parents for the first time and blames his overconfidence on why they do not approve of their relationship (as well as the fact that they are huge homophobes and believe Holt made Kevin gay with his "magic genitalia").
- He and Holt drive to Saratoga Springs every year to get a special English walnut pie, which he (secretly) finds disgusting and considers an abomination.
- He always places trash gently with two hands inside the bin.
- In Safe House, Kevin and Jake watch every Nicholas Cage movie that Jake has ever owned, except for Captain Corelli's Mandolin and Leaving Las Vegas.
- Kevin can still quote the movies from memory, as referenced in The Bimbo.
- He knows self-defense.
- He and Holt attend a hula-hooping class together.
- Kevin may be a smoker like Amy Santiago. In the episode "Cheddar", when the squad loses Holt and Kevin's dog Cheddar, they dress up in Holt and Kevin’s clothes; Jake has a pipe that could be Kevin's.
- He and Holt both consider calling someone a "dirtbag" a compliment, as a dirtbag is an essential part of a vacuum cleaner.
- He has a severe bee allergy.