Absolutely not. It is none of their business and under the American Disabilities Act of 1990 (amended in 2008) an employer cannot force you to disclose any kind of disability unless it affects the kind of work you are doing. Like, if you have to be able to hear to perform your duty or lift 50 pounds, etc., they can hire someone else, unless there's another non-cost prohibitive way you could do the job with some assistance. If you can do the work with reasonable accommodation, they cannot pass you over for a less qualified candidate. Aaaaa, you might want to look into pursuing legal action if you weren't hired due to your mental illness history.

http://www.eeoc.gov/types/ada.html

A couple of details from it:
An individual with a disability is a person who:

• Has a physical or mental impairment that substantially limits one or more major life activities;
• Has a record of such an impairment; or
• Is regarded as having such an impairment.

Title I of the ADA also covers:

• Medical Examinations and Inquiries
  Employers may not ask job applicants about the existence, nature, or severity of a disability. Applicants may be asked about their ability to perform specific job functions. A job offer may be conditioned on the results of a medical examination, but only if the examination is required for all entering employees in similar jobs. Medical examinations of employees must be job related and consistent with the employer's business needs.

So basically, if you can get hired, they can't fire you for already having a mental illness/disability. It's none of their damn business and they can't use it against you even if they do know. That's what insurance is for. If you have a breakdown or sick days or whatever, they can hire a temp to fill your job, but not fire you for being seriously ill (with documentation).