If the "landlord" can prove trespassing or if the "tenant" has an outstanding warrant or gets violent in the "eviction" the police can get involved. 

The pitbull is not violent but is overly rowdy.

LolWhen the term "Bolshevik" fell out of favor in Russia in the 1920's, the extremely violent left changed their moniker to "Communist" to make people happier, but they still killed 10's of millions of people.

I would be inclined to do a general background check and see if there are any violent felonies listed about them.

If you ask me, the most violent place of the 50 states.

Given the behavior of people in crisis, it is reasonable to expect that landlords DO NOT want criminals, especially violent criminals, to rent their units. 

Eugene used to be the "weird" city, now Seattle, Portland, Bellingham, Corvallis, Tacoma, Olympia are all so violent,  drug enslaved, filled with homeless and bad city councils and quickly deep diving to hell, that maybe Eugene has become a top tier compared to them. 

People will think someone violent is in the neighborhood. 

In traditional (ancient) societies, your income depended on a variety of factors, such as your ability to be successfully violent against others, your ability to protect your land, your connections to the king or other powerful people, etc.

If you want to say no violent felony convictions ever and no felony convictions over 5 years fine, it's a policy that treats all renters the same without regards to protected classes.