Either call her on violation of lease(if she is violating it), or he submits an application that you thoroughly vet-credit, criminal checks.

We also use the Colorado Bureau of Investigation which can do a quick online criminal history for about $7.

Is it just the simple fact an eviction exists that I should deny an application, or should I look at the nature and facts of the eviction and consider criminal history before deciding to just deny the application because of the eviction ?

Whether there is a technically legal way to do it or not, I think many people will find the idea itself offensive. 

There's a ton of ways to make money from real estate without ending up in a brick room with "Big bubba" and a bunch of other real criminals or paying ridiculous fines. 

High-quality fake IDs that cannot be detected by the naked eye are readily available to criminals.

He did have a minor criminal conviction for violence a few years ago (I once had a tenant with FIVE DUI'S from out of state.

I’m sure the posters here will give good advice in general, but sounds like you need an expert in real estate AND criminal law to proceed. 

I think even more offensive is not being able to terminate a month to month lease unless your are 1.

Imagine this next sentence in a sassy Texan accent: No offense to those who have mentioned life spans here, but no one can tell you how short your life expectancy is going to be...