Credit, criminal, eviction history.  

Most of the software out there will provide you with the applicant's comprehensive criminal, credit and eviction history.

@Bradley Coleman In order to save yourself a bunch of time you will want to set up minimum qualifications for credit, criminal activity, and eviction history. 

If all looks good credit and criminal-wise and they meet your rental criteria I would 100% rent to them.  

In you invest in D-class properties, well, you should think about having your own organized crime gang to back you up and not worry about legal recourse.I invest in what I'd call C-minus class properties in my area, kept from being D by several factors, chief among which is that Pittsburgh is certainly not criminal-friendly.

Besides doing a criminal background check and credit report, doing things like meeting them in-person, checking to see if their car is clean, and just getting to know them better are some ways to ensure you have a trusting tenant that is a good fit for you and your property.

Fraud: wrongful or criminal deception intended to result in financial or personal gain.

Took in criminals straight out of jail, sex offenders, people with 15 evictions, etc...We used 1/4" luan to patch holes, spray painted everything off white, floors got painted black, kitchen/bath got roll vinyl, no central air (which meant 1 window per room had to function [and that's all the windows that functioned]), busted kitchen cabinetry got boarded over and so on.

I don't know that we've ever received things like criminal background check and credit history reports from sellers.

It may not be a theft under criminal law, but it's still a theft of services and an indicator of someone who has no moral compass.I even live in a landlord-friendly state where evictions are relatively fast and efficient.