Like a lot of New Yorkers, Terry Greiss watched the video of Eric Garner being choked to death by police officers on Staten Island, in 2014, and felt a call to action. But, instead of marching on Union Square, Greiss, the executive director of the Irondale Ensemble Project, a Brooklyn-based theatre company, wrote a letter to Police Commissioner William Bratton. “I said, in a hubristic overstatement, ‘You need what we do. As actors, we train ourselves to really look, to really listen,’ ” he recalled recently. “Within the week, I got a call from 1 Police Plaza, saying, ‘When can you come in and talk about a pilot project?’ I was bowled over.”

Greiss, who has a rumpled white beard and resembles George Carlin, was sitting in the balcony of Irondale’s space, at a church in Fort Greene. The program he developed with the N.Y.P.D., “To Protect, Serve, and Understand,” pairs seven officers and seven civilians for improvisational theatre games. The goal, he said, is to “develop empathy” between the two groups. (It’s unrelated, except in good will, to an initiative to sharpen cops’ visual perception by taking them to art museums.) A few months ago, Greiss put up flyers around the neighborhood and received some thirty applicants, though some of the cops didn’t quite know what they were getting into. “One of our sergeants said that she needed volunteers—I thought it was training,” Jaime Ramirez, an officer in the 73rd precinct, said. He turned to Guy Randel, his partner on the force since 2007. “I was, like, ‘Yo, Guy! Go talk to Sergeant So-and-So and get yourself signed up for training!’ ”

After a communal dinner of mulligatawny soup, the participants stood in a circle onstage. It was their second-to-last workshop before a free public performance; the cops were considered on duty during rehearsals. The civilians ranged in age and attitude, from a twenty-something Black Lives Matter protester to a retired corrections officer. They all warmed up by singing a medieval madrigal in the round, then by collectively keeping a volleyball up in the air as long as possible.

Greiss stood beside a row of assorted hats and announced the evening’s first exercise, called “The Hat Game.” Two players at a time would choose hats and improvise a scene, while trying to snatch the other person’s hat. “Make sure you’re really saying ‘yes’ to every offer,” Greiss reminded them, invoking the cardinal rule of improv, known as “yes, and.” “Someone calls you José, now you’re José.” He added, “Improv is aggressive, O.K.? When you go for something, you’re going with your whole body, your whole mind.”

Randel put on a police hat and played a scene with Annika Sten Pärson, a Swedish-born strategic consultant living in Chelsea, who wore a backward baseball cap. They played the scene as a cop and a vagrant on the street. “Hey, you! Kid!” Randel said. “What you doing over there? Shouldn’t you be in school right now?” As he grabbed her arm, she made for his hat and accidentally slapped him on the forehead.

“That’s assault!” Stephen Barnes (84th Precinct) hollered from the audience, laughing.

Some of the cops were looser onstage than others (Barnes actually minored in theatre before joining the force), and, when there was mumbling, Greiss would yell out, “Share your voice!” The group moved on to a game called “Unrelated Conversation,” in which five players expound on disparate topics of their choice, interrupting one another whenever the urge strikes them. The idea is to concentrate on one thing and not respond directly. Earlene Cowie, an officer in the 79th Precinct, began, “You would think being a police officer I would be paid top dollar. Suffolk County, Nassau County, they all get paid a hundred-something thousand. My paycheck sucks!”

Edward Kelly, a robotics teacher from Sunset Park, cut in, “It’s an interesting career choice, given that I never taught before I worked on computers, and now here I am teaching kids how to build a robot—”

Helen Tazes (88th Precinct) interjected, “ ‘Don’t shoot me! Don’t kill me!’ That’s what I hear from this freaking lunatic! I arrested you because you beat the crap out of someone and it’s on camera, not because you’re black. Not because you’re from a low-income area. I don’t give a shit! I’d rather not arrest you and have to pat you down in your crevices in the July heat!”

Jacqueline Wladis, who works at a fashion startup, jumped in, “You know what sucks? Girls who work in fashion suck.”

More games followed. In “Rants,” six players stood in a semicircle as an organizer called out subjects for them to sound off on, from lint (“Those tape things, they don’t work!”) to Black Lives Matter (“Why does it always have to be involving the police?”) At one point, the instructor called out, “Why are you here?” One by one, the civilians and cops leaped out center stage, interrupting each other:

“I’m here because I’m sick and tired of everyone grouping police officers in one category, like we’re all racists, we’re all here just to lock people up—”

“When I first heard about this, I thought, Oh, man, I get to, like, perform in something? But then I finally heard—”

“I’m here because I want people to know that I see two sides on the story. I’m a cop and also—”

“I’m here because I wanted to make a change in my community. I mean, I’m—”

“Who would pass up this opportunity? Nobody would ever call me to a theatre! But now I have—”

“There are all these stories that need to be told. I think that’s so important. That’s why I’m here, I wanted to—”

“We’re people, too. We have families. We have loved ones. We live in the city we want to be safe—”

“People don’t even respect me! I was respected before. I was referred to as ‘Miss,’ ‘Ma’am.’ Now I’m ‘pig.’ Now I’m ‘racist.’ I am a slew of adverbs, adjectives, nastiness.”

Near the end of the evening, Greiss asked the seven officers to stand onstage holding their police hats. “I want you to look at it, and endow it with what you feel about the job,” he told them. “When you’re ready, put the hat on and let your body respond to the hat.” Postures stiffened; hands rested on hips.

Then Greiss asked the officers to hand their police hats to the civilians. “What does the hat bring up for you?” Greiss asked them. “What does it feel like? How much does it weigh? What does it represent?” The civilians donned the hats. Some looked uneasy, others authoritative. “Officers, watch,” Greiss instructed. “Are they wearing the hat, or is the hat wearing them?”

Richard Gadson, who has been a patrol cop in Bed-Stuy for fifteen years, said, from the first row, “They’re wearing the hat.”