I am a federal probation officer and we have officers here with a variety of degrees. A very common degree for law enforcement is Criminal Justice. We also have officers with degrees in Sociology, Psychology, and Political Science. We also have officers who have completed undergraduate degrees and then obtained their juris doctorate (law degree) and instead of practicing as a lawyer have come to be officers.
Business degrees can also help get you in the door but the public administration and public relations are more kin to working in government positions.
From my experience the type of degree that you attain has minimal bearing on your job as a law enforcement officer. Although some departments prefer a degree in criminal justice or something to that extent, most are looking for a degree showing commitment and ability to drive toward a goal and complete it. Anything you will need to know that will affect your role as a law enforcement officer, will be taught to you when you go through the academy. I'd suggest looking into a degree you think you will enjoy as you will probably be more successful and interested in it.