She had a violent encounter where this person was beating on her door in the middle of the night screaming at her.

In most jurisdictions, threats of violence are no lesser an act than actually committing the violent act. 

One tenant not only could not manage to pay rent, and he was a "bad character": after he lost his job, he first said he could not pay, and then that he would not pay (because the flat has problems), then he became violent and started to threaten the lady next door and her daughter (also my tenant) because she was young, there was some footage of him beating his partner.

I looked up the offense and it was for a violent rape of a 2 year old that resulted in reconstructive surgery for the child. 

If you threaten a member of law enforcement with a knife and resist this is really the best possible outcome where the officer goes home to their family and a violent criminal is off the streets permanently. 

@Ben Morand Criminals need a place to live too...lolAre you looking at violent crime rates?

I'll consider a felony if it was non-violent and 5 years old or more.

I'll echo what David has stated in regards to crime as I do hear of violent crimes in the area.

Hard no on violent offenses even if it is a misdemeanor. 

You can set screening criteria based on things such as credit score requirements, income requirements, violent criminal record requirements, smoking vs non smoking, pets vs non pets (there are laws about emotional support animals too).