Anything else is at best lying to the seller and at worst a criminal act. 

Is there any criminal matter pending against you?""

In most jurisdictions the police won't get involved unless its a criminal matter.I don't know CA law, but here many eviction judges won't do evictions on former owners from a tax sale. 

From the police report, it seems as if the police are getting called there 2-3 times of day from crimes ranging from Criminal Trespass to shots fired, to even Domestic Disputes in the 4 plex I want to invest in

Is breaking the agreement a criminal offense?

However, he has 2 DWI's and 2 speeding tickets on his criminal record.

Things that I look out for when handling rentals are a credit score above 600, 2.5-3x the monthly rent, and a criminal background check.

Its says a lot about their pattern of behavior and the way they are willing to lie and abuse the people they do business with (you and me). 

We use the Premium Tenant screening in Buildium - he had a 735 credit score with no eviction and no criminal. 

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