In most cases, unless there is a dispute as to who was at fault in the accident, the insurance company for the driver who caused the accident will pay the reasonable towing and storage costs (if necessary) of your car. After evaluating the vehicle, if the insurance company declares the car a total loss, they will have the car moved to a wrecking yard or a free storage area. If you refuse to allow the insurance company to move your car, however, you will have to pay the storage costs from the day of your refusal forward, or you can pay to have it towed to your home.