She had a good job, good references, good credit and nothing criminal that I could find.

While, I recognize that breaking and entering is criminal conduct, I also recognize that it is possible to possess abandoned property without violating the law.You are correct that in many States forcible entry is indeed defined to include more than physical breaking.  

A criminal history check only looks at the US. 

i have a couple that is interested in renting, but there seems to be a lot of questions marks, both criminal background checks came listed as in review, he just started a new job 2 months ago, she does not work, and the landlord of the last place they rented sold his home and moved out of the country so he cannot be reached to ask him any questions.

For instance: must qualify on their own, no co-signers, no criminal record, no evictions, good credit, stable income that can be verified, verified previous 2 landlords that are not relatives, etc.

His credit score is 586 and his criminal listed 7 items and his eviction listed one item.

The question is, should i turn in the criminal screening report , or should i just pay the extra $25 as not to open a can of worms in the off chance they don't go as far back as the screening company does?

This week I finally found one that I like for the following reasons:- She is polite, respectful, and reasonable- She is a 5th grade teacher with a steady income over 4x the rent- She has a clean criminal record- She has good credit history and has unintentionally signaled twice that her credit is important to her- Her car and dress seem clean and maintained enough- In some online research I found out she was on the dean's list in college - She is offering to pay another half-month's security deposit to give her an advantage over other applicantsThe biggest concern though is that she has a 75-pound dug that is a mix of Chow, American Terrier, Boxer, and Lab. 

I just looked it up for you but I knew this before anyways, it's pretty common knowledge that criminal and civil crimes have to be tried in the jurisdiction in which they occured or as agreed to in a contract.http://ask-a-lawyer.freeadvice.com/law-questions/can-i-sue-small-claims-co-71943.htm

We use a TPV that does a criminal and credit background check and makes recommendations.