It is illegal to discriminate based on race, religion, sex, etc... a landlord running a credit check on one potential tenant and not the other is an example of discrimination.Other than that, once you've verified your tenant you will feel comfortable handing over the keys to the property.

@Bao Nguyen Good question. 

@Bao Nguyen  Do you at least drive by these properties to check out the neighborhood before you request a showing ?

So you can't mention anything in your ads about race, color, national origin, sex, religion, disability, or familial status. 

We verbally pre-screen them to make sure they don't have evictions or sex offenses or too low of income.

I just ran a search and figured out that a registered sex offender is currently living in one of the units.

As others have mentioned, you have to establish criteria for acceptance and rejection ahead of time and put that into writing; in your criteria, you can say what sorts of offenses are worthy of forgiveness (such as misdemeanors more than 5 years ago) and those unforgivable (sex offense).  

That doesn't mean you should be afraid to say no if you find out he's a sex offender, felon, or has a history of evictions and judgments.

The Fair Employment and Housing Act (FEHA) prohibits harassment and discrimination in employment because of race, color, religion, sex, gender, gender identity, gender expression, sexual orientation, marital status, national origin, ancestry, mental and physical disability, medical condition, age, pregnancy, denial of ... www.dfeh.ca.gov/Publications_FEHADescr.htm Even though the above definition does not specifically state this applies to housing the California Department of Fair Employment and Housing brochure below says as much. http://www.dfeh.ca.gov/res/docs/Publications/DFEH-157H.pdf And yes I agree - bad information is worse than no information.

You can go to your state's online criminal search (if there is one) and perform a search on anybody's name; likewise for sex offender searches.