"I don't believe if a white person was exhibiting this type of behavior that he would be shot down," Burris said. "And that's the disturbing part of this."
Two Sacramento police officers fatally shot Mann on July 11 after responding to calls of a man waving a knife and acting erratically. They say they received reports that Mann had a gun in his waistband, but none was found.
Police Sgt. Bryce Heinlein said in July that the two officers appeared to have been following department protocol when they killed Mann.
Officer Traci Trapani, a police spokeswoman, declined to comment Friday but said three separate investigations into the shooting were ongoing. She said both officers remain on modified duty, assigned to desk work.
The lawsuit, filed in U.S. District Court in Sacramento, claims high-ranking police supervisors condoned the actions with deliberate indifference to police misconduct. It says the officers involved violated Mann's rights by using deadly force against him and deprived the family of their right to a familial relationship with him.
Burris called for police to release the names of the two officers involved and to allow the Mann family to view surveillance video of the incident.
Police have refused requests from The Associated Press to release recordings of 911 calls and video surveillance footage, citing the department's protocol and a law exempting police investigations.
The Sacramento County coroner also would not release Mann's autopsy results or toxicology reports, which are not yet complete, because his death is classified as a homicide.
Sacramento police typically carry tasers, pepper spray and collapsible batons, Heinlein said last month. Supervisors keep two additional nonlethal firearms in the trunks of their squad cars, but Heinlein said in July that the situation arose too quickly for officers to prepare those less-lethal weapons systems.
They did not attempt to use nonlethal weapons before opening fire, nor were they required to do so, he said.
Family members described Mann as a college graduate who was smart, loved politics and economics, and succeeded in several careers before deteriorating into mental illness about five years ago. They said he began having problems after his mother died and had been living on the streets before his death.