You should cross-check the car inspection report done by the company before the shipment to ensure that the damages incurred by your car are not there before you let the auto transporter pick up your car. It is good to have your own inspection report so that you may draw a comparison of the two inspection reports.
If you feel that your car was not handled appropriately during transit, you should get in touch with the auto transport company as soon as possible. Most auto transport companies are eager to solve your problems. If in case the company declines to co-operate, then you can file a report with the Better Business Bureau. Better Business Bureau is an organization that maintains the track of all the companies that have the records of complaints.
If the auto transport company still declines to co-operate even after filing a complaint with the Better Business Bureau, the next step would be to file a legal complaint with the Federal Department of transportation. But be aware of the fact that the Federal Department of transportation may not be able to help you unless you have a court judgement against the company.
It is always advantageous to get help from a legal counselor while you are on a legal process of filing a complaint. It does not mean that you should spend on getting legal help. You can also check with your local county about the available help that you can avail. It is good to sort out things with the auto transport company than to raise it to higher agencies.