The shooting earlier this month sparked days of protests. McClain's family claims police violated his civil rights.
The legal claim is the first step in filing a lawsuit against the City of Pasadena and the police department.
McClain was shot and killed by a Pasadena police officer during a traffic stop.
Police released body cam video last week of the fatal shooting.
The shooting happened Aug. 15 around 8 p.m. when officers made the traffic stop for a vehicle code violation near Raymond Avenue and Grandview Street.
Pasadena police said the driver cooperated with the officers and admitted to driving on a suspended license. But the passenger took off running from the scene.
Vigil held after man shot, killed by police during traffic stop in Pasadena
An officer gave chase and police said the passenger removed a gun from his waistband. That's when the officer opened fire, striking the man.
Pasadena PD released a statement with more information here.
The full video released by the department is slowed down at times to show what officials say is the man reaching for his waistband and holding a gun in his left hand.
Police said the officers could see the gun in his hand as he ran and at one point, he turned to look at the officer over his right shoulder. They said that's when the officer fired twice, thinking the suspect was about to turn and shoot.
After the shots were fired, the man kept running for some time before collapsing onto the sidewalk on Raymond Avenue.
On Thursday, attorney's representing Anthony McClain's father announced they filed the legal claim against the City of Pasadena.
The attorneys claim that McClain was not armed and what police saw was the man's belt buckle, not a gun.
"The evidence will show you that Anthony McClain was unarmed, and what we're saying too, is that we believe that whatever weapon recovered by the City of Pasadena was not actually Anthony McClain's. That's why we're calling on the Attorney General's Office to investigate the Pasadena Police Department, and really conduct an independent investigation about the shooting and what happened to Anthony McClain," said attorney Michael Carrillo.
According to Pasadena Police, the investigation continues. The officer involved in the shooting was placed on administrative leave.
New bodycam video shows fatal officer-involved shooting in Pasadena