OAKLAND -- During a press conference Sunday, prominent civil rights attorney John Burris called for a criminal investigation into the fatal shooting of an unarmed man by the Oakland Police Department.

Burris represents the family of 27-year-old Jody Woodfox, who died early Friday after being shot by police. The family says Oakland police acted with unreasonable force by shooting the unarmed father of two after stopping his car in the 1700 block of Fruitvale Avenue. The family plans to sue the City of Oakland.

Police say the officers involved believed Woodfox was reaching for a gun before they shot him three times in the chest.

"They didn't have no reason to shoot him. He was not armed or nothing. He got out the car with his hands up. When he got out the car, they started shooting. And then he started running," said Shamika Steele, who was in the car with Woodfox. "Given that the crime- at best- may've been a stop for a traffic violation, there was nothing about his conduct that would justify the use of deadly force."

It is the second fatal shooting involving Oakland police in a week and the fifth this year. On July 19. 21 year-old Lesly Allen was shot and killed by police after a car chase. Police found a handgun in the car he was riding in.

During Sunday’s press conference, Burris named the officer who allegedly shot and killed Woodfox as Oakland police officer Hector Jiminez. Burris also claimed Jiminez was involved in a similar officer-involved shooting on New Year's Eve in Oakland. In that case, police shot and killed a man whom they said they believed was reaching for a weapon while crouched behind a car. No gun was found.

"This officer appears to be a very panicky type person. He lacks good judgment and is not the kind of person who should be a member of the Oakland Police Department," said Burris.

Oakland police today declined to comment and would not confirm Jiminez's involvement in this or the New Year's Eve shooting.

But police say the shootings are a reflection of the rising violence on Oakland streets-- in which officers say they are sometimes the target of suspects using cars as weapons.

Chief Wayne Tucker said on Friday that there is still much to be explained about Woodfox's death.

"We're not sure what caused the shooting, what the state of mind of the officers were, what they thought they had," said Tucker.

Burris said he will this week call upon the Alameda County District Attorney's office and the FBI to open a criminal investigation into the shooting.