I would still recommend running credit, criminal and eviction and being specific about your screening criteria.  

No criminal record or evictions.  

You need to run criminal background checks, you need to "attempt" to get names of all the people that will be staying in the house (good luck with that!)

After further consideration, I was pleased to remember that this is a forum for rational and responsible people, not those it-should-be-illegal-to-offend-me folks.My "crime free" lease addendum includes provisions allowing an eviction over suspicion of criminal activity, so I agree with @Chase Gochnauerthat the intent is to deal with disturbances, not provide for a penalty.  

I'm currently a secretary with a Bachelor's Degree in  Criminal Justice. 

Mom and Pop landlord are intentional targets of these criminals and fell victim due to their own short comings.

As far as performing our due diligence can we perform criminal checks or should we keep as far as credit checks ?

I am a Criminal Defense Attorney by trade to I try plan out as much as I can because I hate to be cause off guard.

In the judicial section you can do a criminal conviction and also pending case look-up.

Also depending on your finishes you may end up with renters that have a criminal history.