Here is what I'm doing. I'm currently in the military and became an Auxiliary Police Officer in order to get my proverbial foot in the door prior to applying for full time jobs when my Air Force time is up. There is a number of departments that I'm interested in and I have applied to a couple and will apply to a few more as my separation gets closer. Luckily most of the departments here in the DC area are continuously hiring so I didn't have to worry about that.
Here is my advice. First of all, finish your degree!!!! That will help you be more competitive and you will have a tough time finishing it while you start an LE career. When you get a few months away from graduation, start applying to departments you are interested in.
"Ray, when someone asks you if you're a god, you say YES!"