Is it appropriate for me to ask a postsecondary student what type of disability he has?

DO-IT Factsheet #290
http://www.washington.edu/doit/Stem/articles?290

If a student does not disclose a disability to you, it is generally not appropriate for you to inquire about a possible disability. If a student requests an accommodation, you may ask the student to present appropriate documentation from the campus disability student services office or other designated entity to verify that he has followed your institution's policy for requesting and receiving approval for accommodations. As a staff or faculty member in a postsecondary institution, you are required to provide reasonable accommodations for students with disabilities who request them.

Keep all information pertaining to a student's disability confidential. Contact your disability services office if you have specific questions about disability-related accommodation policies at your postsecondary institution.