That being said, you have to screen based on their credit/criminal/employment/rental history, not your feel or what they say. 

Interestingly, Portugal has extradition to the US, but if this isn’t criminal, maybe that doesn’t matter

Also, there is a service called my SmartMove through transunion where you can check credit and criminal history.

Not paying rent is both unethical, a breach of your agreement and in some cases considered theft of services therefore criminal.

(Preferably one that calls for rental and employment histories as well as simply running eviction/criminal/credit checks).

(I will proceed to file a code violation complaint regarding your fence with Code Enforcement, my Attorney (give him your Attorney's business card) will commence a trespassing civil suit against you seeking $XX,000 in damages and fees), and I will personally call the police and file a criminal trespassing complaint against you with XX law enforcement agency. 

Criminal, background, drug screening etc. 

but this story is complete with criminal elements and creative resolve.  

She submitted an application (incomplete, and that in itself is a red flag, short rental and employment history, but not overly so), but preliminary check through the local courts shows no issues or criminal record. 

It could even be some kind of criminal fraud (deception to obtain something of value aka your rental).