Can my family and their troubles keep me from getting a police job?

I am 21 years old and looking to get into law enforcement. I'm currently working on my bachelors degree. I have never done drugs, and I have really good credit. The thing that makes me nervous is that my father and two brothers are always getting into trouble. It's always something, drugs, shoplifting, DUI's and getting into bar fights. Does the police departments do background checks on applicant's family? Can my family and their troubles keep me from getting a police job?
 
I don't see why it would, as long as you have nothing to do with any of the illegal activities your family is involved with you should be fine.
 
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