The family of Akai Gurley, the unarmed man shot and killed in a Brooklyn housing-project stairwell by a police officer last year, has filed a wrongful-death lawsuit against New York City.

The lawsuit, filed on Thursday in Brooklyn Supreme Court, names the police officer, Peter Liang; the officer’s partner at the time, Shaun Landau; the New York City Housing Authority, which runs the public housing system; and the New York Police Department, along with the city.

Kimberly Ballinger, the domestic partner of Mr. Gurley, brought the lawsuit on behalf of his estate and their 2-year-old daughter, Akaila Gurley.

In November, Officer Liang shot Mr. Gurley, 28, while he and his partner were on a patrol at the Louis H. Pink Houses in the East New York neighborhood. Mr. Gurley and his girlfriend had just entered the darkened staircase on the seventh floor when the two officers entered the eighth-floor stairwell after inspecting the roof. Officer Liang, who had been on the job less than 18 months, unintentionally fired one shot that fatally struck Mr. Gurley in the chest.

Officer Liang was indicted in February on several charges, including second-degree manslaughter and criminally negligent homicide.

Ms. Ballinger’s lawsuit claims that Mr. Liang shot Mr. Gurley “without reason or provocation” and “negligently and recklessly.”

It also says that the housing authority “created a hazardous and traplike condition” by failing to provide adequate lighting in the staircases.

Additionally, the suit charges that the officers did not perform or request medical aid after the shooting. And it says that the city was negligent “in training, hiring, supervision and retention of the police officers involved in this incident” and on training officers on “the use and abuse of power while in the field.”

Ms. Ballinger’s lawyer, Scott Rynecki, said at a news conference on Thursday that the officers had been told to no longer conduct so-called vertical patrols, but were doing so anyway. He added that Mr. Liang had drawn his gun, and that “there was no reason or provocation for having a weapon out of a holster and in the hand.”

Mr. Rynecki said he hoped the lawsuit would lead to some changes, like the city’s hiring an independent auditor to review the training on how officers handle their weapons while on patrol.

“This incident was tragic, and we will review the complaint,” said Nicholas Paolucci, a spokesman for the city’s Law Department.

Ms. Ballinger said that “it’s very hard and difficult to not have Akai in the home,” adding that Akaila asks about her father every day.

“I will be in court every time to make sure that justice for him is kept, that justice for him is received,” Ms. Ballinger said.