The video was grainy, and the men on the street were blurs rendered in black and white. But the clip, recorded by a surveillance camera pointed at a Brooklyn intersection, shows a man approaching the driver’s side window of a car, and then, in an instant, stumbling away before collapsing onto the pavement.

Law enforcement officials said they believed that the video, which circulated late last week, showed the fatal shooting of the man, Delrawn Small, by an off-duty New York City police officer during a traffic dispute on July 4.

“I broke down; I couldn’t stop crying,” Zayanahla Vines, a nephew of Mr. Small, said at a protest in Manhattan on Saturday, recounting his reaction to the footage. “I had to go outside and get a breath of fresh air.”

The clip surfaced as the nation was grappling with videos, broadcast on television and shared widely on social media, of confrontations over the past week between black men and police officers. Mr. Small’s death preceded the fatal shootings of Alton B. Sterling, who was killed early Tuesday by officers in Baton Rouge, La., and Philando Castile, who was killed on Wednesday in Falcon Heights, Minn.

In Mr. Sterling’s case, bystanders recorded the shooting on cellphone video; in Mr. Castile’s, his girlfriend, Diamond Reynolds, broadcast the traffic stop using Facebook Live.

Unlike the other men, Mr. Small, 37, encountered the police officer, identified by law enforcement officials as Wayne Isaacs, when the officer was off duty. The Police Department said that Officer Isaacs, who is also 37, had just completed a 4-p.m.-to-midnight shift and was driving home alone.

The New York State attorney general, Eric T. Schneiderman, has started an investigation into the shooting. A year ago, Gov. Andrew M. Cuomo of New York issued an executive order naming Mr. Schneiderman’s office as a special prosecutor handling police-related civilian deaths.

In a statement issued on Friday, Mr. Schneiderman said the video was being reviewed as part of the investigation. The video was first reported by The New York Post.