., then I would explain that from now on I only deal with the tenant on the lease.And nobody with a criminal record, no matter what. 

And can't you find tenants who don't know criminals the cops are looking for? 

There are tons of online, effective ways to do complete tenant checks (criminal, credit, evictions) - same goes for paying rent online.

Example:"Applicants WILL be denied for any of the following reasons without exception:Past EvictionsAny Felonies or Criminal RecordCredit Score Below ____No Rental HistoryNo or Bad Landlord Referencesetc..."

Establish your screening criteria; income, criminal history, credit, etc. and stick to that.

mhmm i know i love my RED STATES lol i also remember taking a criminal justice course and spending half the semester on intent and long story short is if you have a book bag full of drugs and you can prove you did not know they were there you CAN BEAT THE CASE... never actually happened as far as i know but basically if you grabbed your roommates bag by accident and they came in took the charge and explained it but i don't know anyone who has a room mate that is that nice lol MY POINT IS WHO CARES... not legal advice but if you accepted 2 applications at an open house at the same time and they both say they think they want to move in but are not sure... than you get positive reports for both perspective tenants and they both email you at the same time saying yea they are 100% sure they want it and will have a deposit the next day....

These requirements might not deter a criminal or even an irresponsible person from having a gun, but it could give you additional leverage to terminate a lease or limit your liability if a problem occurred and you could show that the tenant was violating the lease.

Criminal RecordThose are real issues that are truly important.

In fact, cheap enough, be sure they're checking criminal, evictions, employment, landlords, credit, etc.

Criminal and civil charges will not help that.