They are seeking $5 million in damages.
Brisbon's daughter was at a news conference along with the attorney who filed the lawsuit a few weeks ago.
They're alleging excessive force, assault and battery, and wrongful death.
Rumain Brisbon was shot and killed in the doorway of his apartment. Police were investigating a tip that Brisbon was selling drugs, and they say he took off when an officer approached his vehicle.
Police say the two ended up in a scuffle, the officer thought Brisbon was reaching for a gun in his pocket, but it was a bottle of pills.
The Maricopa County Attorney's Office said it would not press charges on the officer.
The attorney for the Brisbon family says police had no probable cause to arrest or detain Brisbon. He says at the time he was shot, Brisbon was neither a fleeing felon or resisting a lawful arrest.
Brisbon's daughter was at the news conference with her mother. Tears streamed down her face; she wore a shirt that said "we will always be daddy's girls, RIP daddy."
"While Rumain Brisbon was on the ground, defendant Rine pointed his weapon and Brisbon, who was unarmed, non-threatening and had his hands up as if he was scared or surrendering, despite his submissive position and Brisbon on the floor of the residence, Rine shot him," said attorney LaShawn Jenkins.
"He was a father, a son, and a friend, and on December 2nd they murdered him and had no reason to, and we just want justice for Rumain," said Mykel Chambers.
An autopsy showed Brisbon was shot twice. Following his death, rallies were held downtown calling for an end to police brutality.