Basically, you can ask any question that actually relates to the applicant's qualifications as a tenant. If you get in trouble from asking any such question, it is your concept of what is a legitimate qualification , not your asking the question. If you ask, say about race, it might be evidence that you discriminate against certain races.
I ask for deifferent categories of information:
1. Personal information, including SS number, drivers license number, place and date of birth. I also ask for address shown on drivers license, and ask to see drivers license. Sometimes, the drivers license shows an address that applicant didn't list.
2. Employment information, including employer, occupation, title (often not the same) and salary. I ask for supervisor's name, but my tenant-screening service doesn't use that. They call the employer directly without a name, to verify employment and salary. I also ask for the same details of previous employment.
3. Former addresses, including present and previous addresses. My service gets references from both.
4. Other financial information, including checking and savings accounts, name and branch of bank and date of opening, credit cards and two personal references.
5. I ask if applicant is a single person, or husband and wife, and how many persons will occupy the apartment. I also ask for names of adults, and names and ages of children to occupy the apartment.
6. I also ask about pets, credit problems, smoking, and if applicant(s) have ever had an unlawful detainer filed against them.