As Marcia mentions, violent criminals are probably ones you would just decline automatically; I would add manufacture and /or distribution of controlled substances and sex offenders at a minimum - consider adding things where repeat offense is very likely or could result in serious trouble for you as the landlord. 

You just have to make sure you're not approving/declining an applicant based on race, color, sex, religion, creed, national or ethnic origin, age, familial or marital status, handicap or disability or sexual orientation.  

What if that felony that they have just been convicted of requires them to register as a sex offender?  

Sam Sendgraff sell the truck and rent a U-Haul when you need to carry big stuff.

We do not discriminate against persons because of race, color, religion, sex, handicap, familial status, national origin, age, sexual orientation, or gender identity.

Well, in CA anyway, we're required to give the Megan's Law database info in our leases, so tenants are aware of it, and can look up sex offenders on their own. 

And was glad to see them move out :-)For instance, I routinely ignored angry voicemails from tenants about how they could hear other tenants having loud sex. 

I found one of my potential tenants was apparently dating a registered sex offender.

Ida Grochowska you need to find a way to get your hands on the actual credit report from one of the 3 bureaus - Experian, Equifax, TransUnion - a criminal background check & sex offender registration and educate yourself on how to read each one.

Getting your first rental property may or may not be as exciting as sex for first time..