Darrien Hunt, 22, was shot to death while carrying a 40-inch samurai-type sword.
that Hunt "lunged" at two officers, Cpl. Matt Schauerhamer and Officer Nicholas Judson and their actions were reasonable. The medical examiner's autopsy report determined Hunt was shot six times, once in the back.
The lawsuit alleges that under the Second Amendment, Hunt had a right to carry the sword and the two officers did not have a right to demand that he surrender.
The suit contends that Hunt was shot while he was fleeing, that police used excessive force and that the officers' actions "manifested malicious, reckless, and callous indifference to the rights and very life of Darrien Hunt."
"They demanded that he give up his sword -- they had no right to do that. He was causing no harm," family attorney Robert Sykes said. "They provoked an incident with this peaceful man."
At a press conference on Friday, Sykes said the family will ask for more than $2 million in damages.
Police and prosecutors say that their actions were justified. And they have rejected claims of racial profiling.
The officers responded to a report of a "suspicious individual walking around a local business with a 'samurai-type' sword," Chief Deputy Tim Taylor of the prosecutor's office said in a statement.
Hunt was speaking with the police officers and was calm and nonconfrontational, according to Utah County Attorney Jeff Buhman.
He then "abruptly and without any apparent provocation withdrew the sword from its sheath and immediately swung or stabbed it toward least one of the officers," Buhman said.
In November, Buhman called the use of deadly force "reasonable" and said that no criminal prosecution would be brought against the officers.
"Preliminary evidence suggests that Mr. Hunt brandished the sword and lunged toward the officers with the sword, at which time Mr. Hunt was shot," Taylor said.
CNN reached out to an attorney for the city, but did not receive an immediate response Friday.
Hunt's mother, Susan, told CNN affiliate KSL
her son was killed because he was black.
"No white boy with a little sword would they shoot while he's running away," she said.