Neither have pets or criminal records.

Well worth the time and effort in my personal opinion.I consider these ex tennats to be criminals and believe they should be brought to justice by landlords.

I am waiitng for the criminal history come back.   

Once I announced that I would require an application fee and run credit/criminal background checks, the calls dropped to a few a week.

She must submit to both credit and criminal reports, so you have all the details to make a decision.

That said, there is a clause in your HAP agreement that says if there is any criminal activity attached to the house you have the right to terminate the lease.  

We all joke that criminals are dumb...

Banks are required to report any transaction $10k+ for routine terrorist / criminal activity checks.Sounds like a pain, going in and paying like in 1952, but shouldn't matter.

Are you in charge of background checks- do you credit and criminal, other states> do you verify, etc.What happens in a hurricane when they can't go in the house for 2 weeks?

I would not consider a co-signer/guarantor if the primary tenant's income was insufficient or if they had other unfavorable traits that I thought they would be a disaster tenant living in the unit (like a prior eviction, criminal record, etc.) -- co-signers cannot help those things.