Forty-three-year-old Carlos Alcis died in August after police officers wrongfully raided his home.
Relatives say police scared the father of eight to death.
They have filed a claim against the NYPD for $10 million in damages.
Police were searching for a man suspected of punching a woman and stealing her cell phone.
Insisting police barged into their apartment in a frightening early morning raid, the distraught family has accused the NYPD of invading their home, a privacy intrusion so startling they believe it might have caused thel heart attack.
"When we woke up there were flashlights in our faces," son Imanuel Alcis said. "We saw 10 police officers in the basement."
The police claim the suspect was seen entering the building. That's when they started knocking on doors.
Police say Carlos Alcis opened his door, and they then questioned the sons and determined they were not suspects.