“Brooklyn Nine-Nine,” the freshman Fox comedy about New York City cops that came up big at the Golden Globes in January, finished out its first season last night having settled into a lovely little groove. Cocky detective Jake Peralta (Andy Samberg) turned out to be talented and a decent friend, not just an irritating hotshot. Captain Ray Holt’s (Andre Braugher) deadpans are just as funny as the muggings of his secretary, Gina Linetti (Chelsea Peretti). Whether the ensemble is running a tactical exercise or trying to talk to Columbia professors at a party, “Brooklyn Nine-Nine” is one of the most pleasurable half hours presently on the television schedule.

(Credit: Eddy Chen/FOX) (Credit: Eddy Chen/FOX)

But in its second season, I think “Brooklyn Nine-Nine” needs to figure out a bigger idea. Just as “Parks and Recreation,” the other comedy from “Brooklyn Nine-Nine” creator Michael Schur, hit its stride when it became an argument for faith in government, “Brooklyn Nine-Nine” needs a theory of the New York Police Department. This is something different from a theory of policing: What “Brooklyn Nine-Nine” needs is not to make the case for the broken windows theory or for CompStat. And I don’t agree with liberal critics of the show who suggest that there is no moral way to make a comedy about the NYPD, given the risk of rendering policies like stop and frisk warm and fuzzy. But “Brooklyn Nine-Nine” will be an even sharper show when it figures out whether it thinks the NYPD functions well or poorly, whether it meets the needs of citizens or not, and whether the precinct it focuses on performs better or worse than the department as a whole.

The best-developed characters in “Brooklyn Nine-Nine” are the ones with the clearest relationships to the NYPD. Holt put up a tremendous struggle to stay in the department during years when it was hostile to him as a black gay man, even though his husband, Kevin, bitterly resents the institution for its cruelty. During a flash-back to Holt’s first day on the job, “Brooklyn Nine-Nine” shows other cops asking Holt “Are you here to turn yourself in?” when he reports for work. His efforts to found an association for gay police officers helped make the NYPD a more diverse, open institution.

But Holt’s long slog to stay and thrive in the department means that he’s a little bit obsessed with the idea of himself as an exemplar, even when he could probably afford to relax. He insists on ties and procedural perfection, which help bring his precinct up to standard. “Brooklyn Nine-Nine” has also hinted, in ways that might be profitably exploited in future story lines, that Holt is afraid to lose his command of the precinct in ways that might compromise his decision-making. “Wint has crazy ties to City Hall,” Jake said during the finale when his captain orders him to lay off a philanthropist with links to the commissioner. “I don’t think Holt would risk giving up his command.” Holt came through to support Jake’s investigation in last night’s episode, but “Brooklyn Nine-Nine” would do well to cultivate the question of just how much One Police Plaza trusts their groundbreaking captain, and what messages he’s gotten about how far his leeway stretches.

While Holt has an uneasy relationship with the institution he outlasted, Jake worships the NYPD: In a flashback, we see him giving an elementary school book report about a hard-boiled account of the department’s exploits in the 1970s. He fantasizes about working mob homicides and making dramatic collars. In one early episode, Peralta arrests a jewel thief he believes is guilty even though he doesn’t have any evidence to support his suspicion, and when the man asks for his lawyer, complains “You have changed! You used to go straight to prison!”

But when Peralta gets a chance to hang out with his hero, “old-school” cop Jimmy Brogan (Stacy Keach), drinking, hanging out in a schvitz, and chasing suspects, Peralta figures out that he prefers the NYPD he actually works in to the department of the past. Brogan is a drunk, a misogynist and a cheerleader for police brutality who dismisses less-abusive and more reliable contemporary policing methods, including data analysis. He’s also the sort of journalist who feels comfortable getting a source drunk to get him to talk. Peralta initially bonds with Brogan, who declares him “one of the last few good cops fighting against the rising tide of hairbags.” By the end of the episode, though, Peralta decides he would rather spot patterns than beat suspects, and that he’s becoming rather fond of Holt, even if the man makes him wear a tie and get his evidence straight first before making arrests. By the end of the season, Jake got assigned to exactly the kind of undercover mob investigation he dreamed of, landing the case by following Holt’s instructions rather than ignoring them.

Fleshing out the supporting characters’ feelings about their jobs, and about the NYPD in particular, would develop our senses of them, and set up conflicts between them and the rest of the department for the coming season. We already know that Rosa Diaz (Stephanie Beatriz) is an aggressive former ballerina, while Amy Santiago (Melissa Fumero) is an eager-to-please goody-goody. But how did these two very different women come to the police department? How did Charles Boyle (Joe Lo Truglio), a mild-mannered foodie, end up a cop? How does Terry Jeffords (Terry Crews), an anxious giant who adores his tiny twin daughters, feel about the relative safety of Brooklyn? And what about Gina, a lackadaisical police secretary who grew up with Jake in Brooklyn before it was trendy?

“Brooklyn Nine-Nine” could also look to “Parks and Recreation”  for ideas on how to set up conflicts between the precinct and the larger NYPD, and between the precinct and the community it serves. In “Parks and Recreation,” the Parks Department contrasts sharply with the incompetent Pawnee City Council and the dilapidated other city agencies. “Brooklyn Nine-Nine” has hinted at this, suggesting that the deputy commissioner is willing to pull rank to protect his son and the philanthropist Peralta investigated in the finale, and it mined real gold from Dean Winters’s performance as The Vulture, a major crimes detective who swoops in and takes over cases that are nearly cracked to boost his own solve average. Deciding whether the Nine-Nine performs better and has more integrity than the NYPD, or whether it’s a precinct full of lovable goofs who haven’t yet reached their potential, will help sharpen the plotting and conflicts on the show, as well as its thinking about big issues in policing.