In situations wherein your physical health is crucial to your job, yes, your employer has a right to order a medical exam (a physical) but I believe what it receives is limited to only what you need to be able to drive. Check with your union or department of labor to get an explanation of what medical results are given to the employer and to whom (if it only goes to the personnel department of the state human resources division in charge of reviewing eligibility of applications submitted for jobs). There still may be medical privacy involved (think HIPAA) for those things that are not relevant to the physical requirements of your job. I assume your employer is looking for things like drug problems, dependencies, back issues, issues of fainting or anything impacting the operation of motor vehicles or heavy machinery.