You do not give up your right to privacy when you apply for a job. Discrimination against mentally ill individuals is alive and well, and while employers can't legally refuse to hire someone with such a disability, they'll find some other reason not to hire you.

If you are asked about your health history, find out what the information is to be used for and who will have access to it before you give it to them. Don't lie, but NEVER volunteer this information. It really is none of their business.