However, in that case consider the elements of criminal trespass. 

My background check includes a criminal records check. 

They are fully documented and fully legal.I don't know if a credit/criminal would show anything but you should definitely require proof of their ITIN to verify identity and their legal status.

Less is more some times. examples: Favorable Fico credit score > than 620 (Suggested) No significant criminal history.

We're able to compensate for that by requiring a co-signer (no double deposits allowed in NH), but the inability to validate identity on the screening platform through questions based on credit bureau records prevented him from being able to complete the eviction and criminal history screening.

You still run credit/criminal, check references, verify income, etc.

I get reports back on their credit, criminal background, income, and eviction record and then it gives you a recommendation to rent or not.  

The criteria we consider (in weighted order): verifiable rental history, income ratio, ability to maintain (income history/savings/assistance), credit score (judgement/collection thresholds) criminal history.

Always take that as a given.Run the criminal check, run the credit check.

Said it could put the property in jeopardy if there was any criminal behavior Since it’s still illegal on a federal level, not worth the risk.