The family of an unarmed Hispanic man fatally shot by US police in 2013 near Los Angeles, California has called for a federal civil rights investigation.

Attorneys for the family of Ricardo Diaz-Zeferino, 34, and a second man injured in the shooting filed a letter on Wednesday asking the Justice Department to investigate the Gardena Police Department.

"This is a poster child case as to why police departments cannot control their own officers, and why there's no discipline and no supervision, no investigation, and it's all controlled by the lawyers who defend the police officers," said attorney R. Samuel Paz.

The attorneys wrote that Gardena police consistently violate their own policies and California state laws by failing to internally investigate fatal police-involved shootings, including Diaz-Zeferino.

They cite 10 other shooting deaths involving the Gardena police department since 2009.

The plea comes after a federal court ordered the city of Gardena to unseal the footage of the 2013 shooting.

Video footage recorded from three police-car cameras shows the shooting death of Diaz-Zeferino, who was stopped with two of his Latino friends by police investigating a bicycle theft on June 2, 2013.

The stolen bike belonged to Diaz-Zeferino's brother and he was trying to find it, but he was shot when he did not obey officers' commands to stand still with his hands in the air. Diaz-Zeferino was shot eight times, and Eutiquio Acevedo Mendez was shot once.

"The police didn't listen," Acevedo-Mendez said during a Wednesday news conference. "All they had to do was look. Not one police who fired stopped to search us."

The request for a federal civil rights investigation comes amid intense public scrutiny of police shootings across the United States.

A poll released earlier this year has found a significant distrust of police in the United States, where many Americans believe police target minorities unfairly and often lie for their own interests.