Your insurance company's claim adjuster should investigate your claim and get estimates on the damage the thief caused to your vehicle. Since the car was stolen you would place the claim under your comprehensive coverage.

The claims adjuster will determine from the damage to the vehicle if it will be declared a total loss or if it will be repaired. If they decide to repair it, due to the damages not be substantial enough to find the car totaled, and you have safety concerns after it is repaired you can bring them up to your insurance provider.

Normally though if your car is repaired and given back to you and you decide you no longer feel safe in it, you cannot hand it over to the insurance company but instead will need to sell it if you do not want to drive it because of these concerns.