The lawsuit names the city, the two officers involved and the housing authority, which runs the apartment building where Akai Gurley, 28, was killed in November 2014.
The lawsuit was brought by Gurley's domestic partner Kimberly Ballinger on behalf of his estate and their toddler daughter at the Brooklyn Supreme Court, their lawyer said.
His death was one of a string of recent incidents in which police officers killed black men under questionable circumstances, sparking angry and at times violent protests across America.
Officer Peter Liang has been charged with manslaughter, criminally negligent homicide, assault, reckless endangerment and official misconduct. He faces up to 15 years in jail if convicted.
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After Liang discharged the bullet, reports said that he and his then partner Shaun Landau did not respond to radio contact for more than 6.5 minutes nor did they call for medical assistance.
Lawyer Scott Rynecki did not specify how much he was seeking, saying that New York law prohibits an amount being put in the complaint.
His partner was also named. "We've been given some information that indicates after the shooting they did not timely call for an ambulance or provide medical care," Rynecki said.
The city of New York was named as Liang's employer, and the housing authority because it had a duty to maintain the premises where the stairwell allegedly had no lights, Rynecki added.
Ballinger, a home health aide, includes a clause of action on behalf of the couple's young daughter for the loss of her father.