The family of Dwayne Jeune met with the Acting Brooklyn District Attorney to demand police reform on Thursday.
The 32-year-old was shot and killed by Officer Miguel Gonzalez last month after his mother called 911.
She said he was emotionally disturbed and nonviolent.
The NYPD says he charged at officers with a kitchen knife, prompting Gonzalez to open fire multiple times.
City Councilman Jumaane Williams says Jeune's case demonstrates the need for change in the department.
"This is the reason we need to unfold the body-cams at a much quicker pace than what's happening," Williams said. "So that when there's a dispute like this we can all look at the same thing.
"The next step will be for the District Attorney's office to conduct its investigation of this killing of an emotionally disturbed man," said Jeune family attorney Sanford Rubenstein. "The family called 911 for help because he was acting erratically, and he ended up, instead of being helped, dead. This should not be happening in this city."
Officer Gonzalez was involved in another shooting death of an emotionally disturbed person last year.