The lights were on the vehicle’s passenger-side visor, where an officer would mount them but they were clearly not department-issued lights, he said. Captain Taylor was driving his personal vehicle, still on his way to work, he said, and so he could not perform a car stop. He reached for his police radio to call it in when the Acadia turned off Bath Avenue.

“I put over the air that I needed some assistance,” he said. Soon after — “20 seconds,” he said — four police cars converged around the Acadia. “I got out and pointed to the car, ‘Here’s the guy,’ ” Captain Taylor said.

Cases of police impersonations have kept the real police busy in recent months. In February, two men who were arrested after a strong-arm robbery in Spanish Harlem in Manhattan turned out to be members of the auxiliary police — unarmed volunteers — posing as officers. They beat and handcuffed a deliveryman from a Chinese restaurant and took his money, the police said.

In October, a woman walking to a store for cigarettes in Bedford-Stuyvesant, Brooklyn, was stopped by a man in a car who beckoned her inside, saying he knew where to get some. She did, and he spoke into a hand-held radio, using police jargon, the police said. He pulled over and demanded sex, saying he would arrest her if she did not comply, the police said. She did, and later escaped. Officers arrested a man identified as Walter Barnes, 47, of Flatlands, Brooklyn, charging him with rape and police impersonation.

Another man, identified as Francisco Rivera, 29, of Jamaica, Queens, was arrested twice for raping or assaulting women in motel rooms after identifying himself as a police officer, in October and November, the police said.