The suit, filed Tuesday in Louisiana state court, claims the two white officers who encountered Sterling, who is black, on July 5, at a Baton Rouge convenience store used unnecessary force.
The suit's claims mirror allegations that federal prosecutors weighed when they considered -- but last month declined
-- to lodge civil rights charges against Officers Blaine Salamoni and Howie Lake II. Those case files were handed over to Louisiana Attorney General Jeff Landry, who is contemplating charges.
Without divulging specifics, the suit highlights a letter sent May 25 to Police Chief Carl Dabadie in which Baton Rouge Mayor Sharon Weston Broome refers to "very disturbing details surrounding the actions of Officer Salamoni" that both officials received "during a consultation with the Department of Justice."
Salamoni's "termination is warranted," writes Broome, who notes she was "shocked and appalled by this information."
The Baton Rouge Police Department declined to comment on the lawsuit, citing "pending litigation," Sgt. Don Coppola told CNN. Salamoni and Lake remain on paid administrative leave, he said.
The Sterling family's lawsuit names as defendants the city of Baton Rouge and its police department, along with Dabadie, Salamoni, Lake and the department's liability insurer.
The lawsuit, which seeks an undisclosed amount for punitive damages, comes on the heels of settlements this month in two other high-profile cases that left black men dead at the hands of police.
The family of Philando Castile, who was shot and killed last year by a St. Anthony, Minnesota, police officer, reached a $3 million settlement with the city
days after the officer in that case was acquitted of second-degree manslaughter
. The family of Michael Brown, who was shot and killed in 2014 by a police officer in Ferguson, Missouri, settled its wrongful death lawsuit
against that city for an undisclosed amount.
'Tolerating racist behavior'
Sterling, 37, was selling CDs and DVDs outside the Triple S Food Market when the officers approached him in response to a 911 call that a man with a gun was near the store. Sterling "displayed no aggressive behavior or manners," the suit claims. Sterling at the time was carrying a .38-caliber revolver, with six rounds in it, the Justice Department has said.
Almost immediately, Salamoni pointed his service weapon at Sterling's head and yelled, "B**ch I will f***ing kill you," "I am going to shoot you in your mother f***ing head," the suit claims.
The officer should have known that the "continued escalation and provocation would have caused a negative encounter with Mr. Sterling," the suit states.
"In less than one second, Officer Salamoni yelled at Mr. Sterling and then pulled his gun and fired three shots into Mr. Sterling's chest," it states. "Officer Salamoni then fired three more rounds needlessly and excessively into the back of Mr. Sterling."
The fact that Lake did not fire a single round proves that Sterling was not an imminent risk, the lawsuit notes, adding that the officers did not render "urgent medical care or first aid" after mortally wounding Sterling.
The suit also takes aim at Dabadie, claiming the police chief failed to properly "train all active police officers under his control and supervision."
Dabadie's department "failed to have a written policy on the use of deadly force, and has a history of incidents of excessive force, racism in the BRPD towards members of the African American community and inadequate oversight by decision makers in the BRPD and the City," the suit states.
The suit accuses the department of having "a long standing pervasive policy of tolerating racist behavior of some of its officers." It cites local news reports of alleged racist behavior by Baton Rouge officers beginning shortly after Hurricane Katrina and continuing through protests that followed last month's Justice Department announcement.
It also claims the city "did not properly examine and scrutinize the backgrounds of Officers Lake and Salamoni."