The crash, involving a Peugeot 206 and a Ford Transit van, occurred last Wednesday in Upperton Road, Leicester.
Two passengers in the car died at the scene and the driver has now been discharged from hospital.
The 35-year-old man was bailed pending further inquiries.
Updates on this story and more from Leicestershire
The Peugeot driver suffered serious injuries, while two people in the truck sustained minor injuries in the crash, which caused damage to a shop on the corner of Upperton Road.
The incident has been referred to the Independent Police Complaints Commission (IPCC), Leicestershire Police said.
A man has been arrested on suspicion of causing death by dangerous driving after two men died when a car being followed by an unmarked police vehicle collided with a tipper truck.