Can stating that I have a mental illness on a juror questionnaire affect my chances of future employment?

Juror questionaires are public and anyone can see them. However, the odds of some prospective employer finding them, in even the most thorough background check, is very slim. Many prospective employers will ask the same question themselves and will ask for a release so that they can get your medical records, and will not hire someome who refuses, but that was not your question.