Crump said in a statement that accompanied the complaint: "The City of Minneapolis has a history of policies, procedures and deliberate indifference that violates the rights of arrestees, particularly Black men, and highlights the need for officer training and discipline."
Floyd, a Black man who was handcuffed, died on 25 May after Derek Chauvin, a white police officer, allegedly pressed his knee against Floyd's neck for nearly nine minutes as Floyd said he could not breathe.
Chauvin has been charged with second-degree murder, third-degree murder and manslaughter. Three other officers at the scene - Tou Thao, Thomas Lane and J Kueng - have been charged with aiding and abetting both second-degree murder and manslaughter.
All four officers were fired the day after Floyd's death, which set off protests that spread around the world and turned into a national reckoning on race in the US.
Floyd's death also sparked calls to abolish the Minneapolis Police Department and replace it with a new public safety department. A majority of City Council members support the move, saying the department has a long history and culture of brutality that has resisted change.
A public hearing was planned later on Wednesday on the proposal, which requires a change in the city's charter that could go to voters in November.
The lawsuit came on the same day a court allowed public viewing by appointment of video footage from the body cameras of Lane and Kueng.
A coalition of news organisations and attorneys for Lane and Kueng has been advocating to make the videos public, saying they would provide a more complete picture of what happened when Floyd was taken into custody. The judge hasn't said why he's not allowing the video to be disseminated more widely.
According to documents in state probate court, Floyd is survived by 11 known heirs, including five children and six siblings. They live in Texas, North Carolina, Florida and New York. All but one of Floyd's children are adults. He has no living parents or grandparents.