Answered by Susan, Hiring Expert at Praxair, Inc., on Monday, September 16, 2013
This is difficult to answer not knowing what job you are doing in the car dealership.
I can see certain jobs which require driving (and therefore you are insured by the Company's auto insurance policy), to require the employee to be "fit" to drive safely. If that is the case, they may require medical background checks to comply with their insurance regulations.
I think it would be fine for you to ask your company why they require this information, and also who would have access to the information (to give yourself piece of mind around confidentiality).