Investigators released body-worn camera video showing the deadly encounter earlier this year.
The shooting happened on December 9.
Video showed Chicago police responding to the 5700 block of North Washtenaw in West Ridge for reports of a stolen vehicle.
Investigators say the officers found two people trying to enter the vehicle. As they ordered the people to stop, video showed one person run while the other tried to get into the vehicle.
A struggle then took place. That's when one shot was fired before the officer was briefly dragged by the car, which then crashed.
Roberto Calvario Jr., 20, of Albany Park died at the scene, officials said.
Lawyers for his family said Wednesday that officers were responding to a call that had nothing to do with Calvario, but he was in a vehicle nearby. They say the officer attacked Calvario and shot him.
On Wednesday, the Chicago Police Department said it had not received the lawsuit and does not comment on pending litigation.
The officer involved in the incident has recovered from his injuries.
Two weapons were found at the scene, police said at the time.
The Civilian Office of Police Accountability is still investigating the police-involved shooting.