| Normally no, there can be a few exceptions. In TN for example because they were hired by a family member, there were a couple on the Highway Patrol there.
And the exact crime may make a difference, how long it has been and more. For example some departments have a strict rule, any drug use, convicted or not, will kick you out,
Also no one with a domestic violence change can be a law enforcement since it effects your ability to carry a weapon.
So unless you have some connections, and unless you don't mind working at small departments with low pay and no benifits, I would say another line of work would be best. | 
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