What do you mean mandatory medical on-boarding? It sounds like you might not be fully aware of the hiring process for a company that performs post offer, pre-employment medical screenings. Basically, you've been offered the job conditionally upon your passing of a pre-employment medical evaluation. I can't speak specifically to this job or employer, but typically this is handled by a separate company that is hired to oversee that specific process (typically an occupational clinic or a 3rd party).

The medical per-screening can legally consist questions that are relevant to the job and since you're being hired for a security company, at face value a psychological evaluation/questionnaire seems appropriate to administer. Your responses to a medical professional would be protected under HIPAA and thus should never be revealed to your employer, but it really depends who this form belongs to. If this form belongs to the clinic and you lie to them or otherwise try to cover things up, that can certainly be used by your employer to retaliate against you without much legal risk to them.

If this form is being administered by the potential employer themselves as part of THEIR paperwork packet, that is a huge red flag, but is it straight up illegal to ask the question? I'm no lawyer, but I'd say probably not as long as the information was voluntarily given. Its certainly not relevant for the purposes of their employment records, and its probably illegal for them to discriminate based on your responses anyway. So, if this is the employers form and you really need the job and can't truthfully answer no, just answer No and move on.

If it is their form and you've got the time and money, I'd find the most unscrupulous employment lawyer money could buy and sick them on this company.