This question is about pre employment physical.
Can an employer require a physical?
Yes, an employer can require a physical. The key is that you have to have been offered the job before they request the physical. It's a post-offer, pre-employment situation, and that means you need to pass the physical to actually be hired, but they're willing to hire you if you do.
It's important to note that a drug or alcohol test is not considered part of a medical exam. You're likely to get one with your medical exam, but because it's a different classification, a potential employer can require this test outside of the exam and before they offer you any job.
But because some medications can alter a drug test, most employers wait until post-offer for this so they can get the whole picture.
Some other rules come into play when a physical is required for a job. It needs to be a requirement for all people who are potentially being offered the job, and if someone has a disability, appropriate accommodations must be made for them to take the physical also.
Beyond that, your medical record is still confidential and kept separate from other employment records.