Tyre Nichols, a 29-year-old father of a four-year-old boy, died in hospital on January 10 of injuries suffered during his arrest by five officers, all of whom have been fired.
"He was a human pinata for those police officers," said lawyer Tony Romanucci, Crump's co-counsel.
The department determined that the officers violated multiple policies, including using excessive force, failing to intervene and failing to render aid.
Crump said the video reminded him of how Los Angeles police repeatedly beat King in video captured by a witness in 1991, sparking protests and reforms in the department.
"Regrettably, it reminded us of (the) Rodney King video," said Crump, who previously represented the families of George Floyd and Trayvon Martin.
"Regrettably, unlike Rodney King, Tyre didn't survive."
Nichols was less than 100 metres from home during the traffic stop in the Tennessee city and called out for this mother three times at the end of the video, Crump told a news conference.
Crump viewed the police bodycam video with Nichols' family, later telling reporters that local, state and federal investigators promised to release the video to the public within a week or two.
The Tennessee Bureau of Investigations, FBI and Justice Department are among the agencies investigating the incident.
Memphis police were co-operating, Chief Cerelyn Davis said.
Nichols' family said his injuries included brain swelling and kidney failure and was placed on dialysis before he died, according to the Commercial Appeal newspaper.
Relatives told WREG television it was especially hurtful because all the officers involved were black.
A photo of a bloodied, intubated Nichols was released to the public. It helped fuel multiple days of protests and calls of "Justice for Tyre" in Memphis, a city with a majority black population.
Memphis police identified the former officers as Tadarrius Bean, Demetrius Haley, Emmitt Martin III, Desmond Mills Jr and Justin Smith.
