Does the past owner have a criminal record for violence, arson, etc.? 

Now those charges didn't go anywhere, but I think the threat of criminal prosecution will most people.  

In our criminal system, you are innocent until proven guilty hence you really can't do anything until you have proof of it.

She was very afraid of moving to this neighborhood because there was a strong belief among Americans and Russian-speaking immigrants that this neighborhood was criminal, full of murderers, drug dealers, and thieves.

Will the inspector or the courts eventually come after me and press criminal charges?

Id suggest filing criminal reports with the appropriate authorities asap.

Then I moved to a program primarily for young men with developmental disabilities but highly functional, like working at Home Depot and Fed Ex who had some criminal histories so had to be supervised, now I’m at a transitional housing facility.

The response made us feel criminal.

What resources do I need to effectively screen tenants, how do I run their credit or criminal history?

Once we have a completed application, we verify income (by calling the employer and/or with paystubs), verify previous address history (this will show up on the credit check, we ask about any addresses that show up on the credit check but are not listed on their application), and verify identity by requesting a copy of their photo ID to make sure their info matches the application and screening reports.Next, we run credit, criminal, and eviction reports.