In your scenario, you should place a sign on your car that reads "STEAL ME!" before running into the house.
A few years ago, there was a police pursuit of a "traffic violator". The officers in the pursuit were able to get the license plate of the vehicle, and the dispatcher ran it for "wants & warrants". It came back "clean", but....a few seconds later, an officer blared out over the police radio, "Don't shoot it! That's MY car!".
The pursuit didn't last very long, and the driver/suspect was taken into custody without any problems. It turned out that he (the suspect) had hopped a wall and "jimmied" the door of the car, then he disabled the steering wheel locking device and "hot-wired" the ignition. The suspect was unaware of the fact that the wall he had climbed over surrounded a police station where officers were allowed to park their privately-owned vehicles!
Shoot at your OWN car to "mark it for I.D."? HAHA! Cars have more "I.D." marks on them than you may be aware of! Besides the license plates and vehicle identification number (VIN), there are several "hidden" VIN numbers in various locations of ALL vehicles.