Two passengers in a Peugeot 206 suffered fatal injuries in the crash on 10 March on Upperton Road, Leicester.
They have been named by police as David Anger, 24, and Christopher Needham, 37, both from Leicester.
A 35-year-old man arrested on suspicion of causing death by dangerous driving has been released on bail.
Updates on this story and more from Leicestershire
The Peugeot driver suffered serious injuries but has since been discharged from hospital. Two people in the truck sustained minor injuries in the crash, which caused damage to a nearby shop.
The incident has been referred to the Independent Police Complaints Commission (IPCC), Leicestershire Police said.
Two men who died when a car being followed by an unmarked police vehicle collided with a tipper truck have been named.