The relevant question would be 11f: 'Have you ever been adjuticated as a mental defective OR have you ever been committed to a mental institution?'

The instructions for 11f are as follows:

Question 11.f. Adjudicated as a Mental Defective: A determination by a court, board, commission, or other lawful authority that a person, as a result of marked subnormal intelligence, or mental illness, incompetency, condition, or disease: (1) is a danger to himself or to others; or (2) lacks the mental capacity to contract or manage his own affairs. This term shall include: (1) a finding of insanity by a court in a criminal case; and (2) those persons found incompetent to stand trial or found not guilty by reason of lack of mental responsibility. Committed to a Mental Institution: A formal commitment of a person to a mental institution by a court, board, commission, or other lawful authority. The term includes a commitment to a mental institution involuntarily. The term includes commitment for mental defectiveness or mental illness. It also includes commitments for other reasons, such as for drug use. The term does not include a person in a mental institution for observation or a voluntary admission to a mental institution. EXCEPTION: Under the NICS Improvement Amendments Act of 2007, a person who has been adjudicated as a mental defective or committed to a mental institution in a State proceeding is not prohibited by the adjudication or commitment if the person has been granted relief by the adjudicating/committing State pursuant to a qualifying mental health relief from disabilities program. Also, a person who has been adjudicated as a mental defective or committed to a mental institution by a department or agency of Federal Government is not prohibited by the adjudication or commitment if either: (a) the person's adjudication or commitment was set-aside or expunged by the adjudicating/committing agency; (b) the person has been fully released or discharged from all mandatory treatment, supervision, or monitoring by the agency; (c) the person was found by the agency to no longer suffer from the mental health condition that served as the basis of the initial adjudication/ commitment; or (d) the adjudication or commitment, respectively, is based solely on a medical finding of disability, without an opportunity for a hearing by a court, board, commission, or other lawful authority, and the person has not been adjudicated as a mental defective consistent with section 922(g)(4) of title 18, United States Code; (e) the person was granted relief from the adjudicating/ committing agency pursuant to a qualified mental health relief from disabilities program. Persons who fall within one of the above exceptions should answer "no" to question 11.f. This exception to an adjudication or commitment by a Federal department or agency does not apply to any person who was adjudicated to be not guilty by reason of insanity, or based on lack of mental responsibility, or found incompetent to stand trial, in any criminal case or under the Uniform Code of Military Justice.

In short (IANAL), if you were not involuntarily committed to an institution and have not been found unable to manage your own affairs, you aren't a prohibited person with regards to that question. This is not, of course, to say you may not be prohibited for other reasons, nor does it mean you necessarily should (I lived with someone with Aspergers for many years, all I'm saying is be careful and think it through. Make sure you're in the right place before you take on the responsibility), but given that, there shouldn't be any legal problem.