I am a little surprised how many people are totally fine with having a grandmother and three grand kids removed by the cops and slapped with a criminal charge.

Then the criminal and eviction reports definitely still need to be run on the tenant.To keep payments consistent and timely, insist on auto debit from their checking account, or ideally their parents checking account.  

Section 8 is a two edged sword that helps people that want to improve their lives, yet creates mobility for bad people to enter neighborhoods that are not accustomed to criminal lifestyles. 

Verify they are students in good standing and do background/criminal/credit checks, but only put the student on the lease.  

I just want to know she isn't a criminal with a history of evictions.

These are generally around credit, criminal, and evictions but could expand for instance to your pet policy and or smoking etc..  

You can be just as tough on requirements for good credit, no criminal, no eviction, good references, etc.  

This is my best tip for a first timer on selecting the best tenant: (copied this from my previous post)I used the tenant screening tool provided here on BP "smartmove" It provides a criminal background check, an eviction check and credit check.

What if he is trying to hide a criminal background?

Basically, your policy has to have a reason for saying no to criminal offenses, and your policy can't be more discriminatory towards one race than another.The document says that discriminating against criminals can be harder on blacks and hispanics than other races.