Checks State and county criminal records, sexual offender, terrorist watch, credit check, bankruptcy.

I've always found it ironic that gays walk around touting their sexual preference while normal people don't go around talking constantly about their sex lives.

For example, rent on time or early for all periods (weekly or monthly) in the past 12 months; no disturbances; repairs for tenant caused damages paid by tenant; informing landlord of misbehavior by other tenants; and I'm sure you can come up with more.

We list no violent, sexual, or drug convictions and that we have the right to refuse to rent based on any felony conviction on our postings.

There were several LLs of class C multifamily properties that would take felons and  sexual offenders in the area where he worked. 

Young/old people are just as much a protected class as anyone of race, sexual preference etc.

I have a one page cover sheet I add to each application with check boxes to show that they have the "deal breaker criteria", a section to score the "nice to have" criteria, and a section to briefly explain my acceptance or rejection.Our Criteria: Complete applicationVerifiable rental historySufficient income/resources to pay rent and liveCredit report showing prior addresses consistent with application We do not deny housing for race, color, religion, sex, national origin, handicap, sexual orientation, marital status, or familial status.We do deny housing to individuals:convicted of manufacturing or selling drugsconvicted of a crime the poses a threat to the property or neighborhood, including repeated disturbances, gambling, prostitution, violence, threats of violence, or rapewhere there is poor prior tenancy: evictions, violations, damage to rental property, poorly handled move outs, amounts are still owing to landlords or utilities.who misrepresent information on the rental application

A year later,  she was being sexually harassed at her job so she quit.  

If they can't provide proper proof of income, or if they have more family members than your municipality allows in your apartment, or if they are felons, sexual predators, or other classes that your locale allows you to restrict applications based on, then good.  

Prohibited in all states is the refusal to rent because of ethnic background, race, religion, sex, sexual proclivity, age, marital status, or income source.