I would think that such medical information would be protected via HIPAA unless you authorize access during a background check, etc. But even then I'm pretty sure they're mostly looking for criminal offenses, not medical issues.
employee health is allowed to ask you to list your medications but this does not go to your supervisor and is only asked after you have already been hired. it is illegal for any employer to ask what medications you are on (psych or otherwise) or if you have any medical problems that does not pertain to your job. It is routine in eras/residency/fellowship/attending applications for you to be asked if you have a medical condition that would interfere with your ability to perform that job. If you do not feel that your psych condition would interfere with your ability to perform, then you would not be expected to list it.
I wouldn't be particulary concerned in applying for a hospital job since, as mentioned, you'll be protected by employment law.
If you mean hired as a physician, however, I'd err on the side of caution when you apply for licensure. You may think your condition doesn't affect your ability to practice medicine, but if you have a significant diagnosis some states, Texas as a notable example, will place some supervision requirements on your license for the first few years (they'll ask for reports from your therapist and your employer, etc). If there are no problems, that's the end of it. If the licensure board hears later on that you had a condition that they would have wanted disclosed - and you didn't disclose it, there can be real hell to pay.