An African American, Daniel Prude, 41, died in New York State after being hooded by police and held face down to the road for two minutes.
Body camera footage showed police using a “spit hood” on his head.
He later died of asphyxiation but his story has only now been made public.
His death was two months before the killing of George Floyd.
Mr Floyd died after a white policeman knelt on his neck for nearly eight minutes in Minnesota. Anti-racism protests broke out in the US and globally in the wake of his killing.
A warehouse worker from Chicago and father of five, Daniel Prude was visiting his brother at the time of his death.
Mr Prude’s brother, Joe, said he called police in Rochester on 23 March as his sibling was showing acute mental health problems.
“I placed a phone call for my brother to get help, not for my brother to get lynched,” he said at a new conference.
Police body camera footage obtained by the family through a public records request shows Mr Prude, who had been running naked through the streets in a light snow before police arrived, lying unarmed as officers restrain him on the ground.
The video shows that Mr Prude complied immediately when officers arrived on the scene and ordered him to lie on the ground and put his hands behind his back. He can be heard saying: “Sure thing, sure thing.”
He becomes agitated, at times swearing at the officers who surround him and spitting, but he does not appear to offer any physical resistance, according to the footage.
Mr Prude told officers he was infected with coronavirus, and they placed a white “spit hood” over his head.
One officer is seen pressing down with both hands on Mr Prude’s head and saying: “Stop spitting.”
After he stops writhing and goes quiet, one officer notes: “He feels pretty cold.”
Medics try to revive him before he is carried into an ambulance. He was taken off life support a week later on 30 March.
The family’s lawyer said the reason the case was not made public earlier was that it had taken “months” for police footage to be released.
According to a post-mortem examination report seen by the Rochester-based Democrat and Chronicle newspaper, Mr Prude’s death was a homicide caused by “complications of asphyxia in the setting of physical restraint”.
The report also listed PCP, a strong hallucinogenic drug, as a complication.
New York state’s attorney general called the death a “tragedy” and said an investigation was under way.
Mr Prude’s brother called his death “cold-blooded murder”. “How many more brothers gotta die for society to understand this needs to stop?” he added at the news conference.
Lawyers for the family are in the process of filing a wrongful death suit.
The family have also called for the firing and arrest of the officers, US media report.