Our state has one with a $20/person fee to get criminal, credit (not the score, but the details and a "fitness score"), and they phone to verify income source.  

@Michelle I Massey this isnt Facebook.... yes, they can refuse to rent to you based on your criminal history.

He does have a stable job, pretty good credit, no criminal convictions (that I know of), and is generally a honorable person (as in I lent him money in the past and it was always paid back with interest).

If you have been a victim it is important to let that be known now so we can get this taken care of before your situation worsens as they abandonship.The city has commited to an active role in persuing criminal and civil penalties against them.

Hopefully if they are as dumb as the average criminal they will be caught.

We will not be liable for failure to provide security services or for the criminal or wrongful acts of others.

Kinda like getting your driver license.. without knowing the " traffic laws " you may be able to drive ok.. but when you get pulled over by the cops they will explain what traffic offence you did not know your getting the ticket for.. eh ?

Are there any resources out there that could provide some screening of these persons for things like criminal records,...etc?  

It sounds like you may have either a credit criminal, or someone who has no real ability to repay, both of which could, and should, have been screened for.

I have never had a break in attempt or any significant criminal event on my property.