Here in Southern California, currently a degree is desirable but not many agencies I am aware of require one anymore just to get your foot in the door. A degree does; however, look good on your application. If it comes down to an applicant with a degree getting hired vs. one without a degree? Degree gets it every time! It will also help you promote through the Department.
A much BIGGER attraction is military service! Even Reserves looks good on paper. It shows you have commitment and discipline and demonstrates honor and integrity, key components to a successful law enforcement career. Degree vs. military service? Military service gets hired every time.
Lastly, most agencies have a police reserve program. I highly suggest this route for two reasons. You get a taste of law enforcement to see if it really is for you and and No. 2, having been a reserve is VERY attractive to a police Department recruiter, especially the agency where you were a Reserve.
I hope my answers have helped and good luck. Not an easy career choice but a very rewarding one!