I think it would depend on the specifics of the criminal background. However, I can't imagine what it would be that would prevent you from doing what you want. I was looking at a couple of the online options for law enforcement education, and none of the forms ask for history on family members. So, I would not foresee any problems with you going to school, and then becoming an officer. http://www.publicsafetydegrees.com/criminal-justice-degrees.php