Do real life police ever actually run out in the street, show their badge, and take someone’s car in order to chase a suspect? Is this or would it be legal?
And if it does happen, does insurance cover this? Does the police department pay for the vehical?
It can happen but extremely unlikely. In Arizona if a sworn peace officer asks a civian for help they are automatically deputized. This makes the department liable for any fuckup that person may do. By the same token the department would be liable for any property damage.