A college degree will serve multiple purposes: It can overcome a past that contains some stupid mistakes, it can provide for career advancement and financial incentives while in law enforcement, and can also open doors to additional opportunities outside of law enforcement (teaching, consulting, academy instructor, etc.). It can be of great benefit in a career where a good number of one's peers will not have that. In my state, college is required for promotion to sergeant - at least to the equivalent level of an AA/AS degree - and moving higher will generally require a BA/BS or greater.
My recommendation is NOT to get that degree in "Criminal Justice," however, as most any police applicant with a degree will have that particular one. I typically recommend that youngsters go for something that also has applicability outside of law enforcement as well as within. Sociology, Psychology, Public Administration, Education, Criminology (a science), various Law, Communications, or Political degrees as well. As one who has culled backgrounds for many years, I can tell you that when an applicant lists a degree OTHER than "Criminology," he or she stands out. I also recommend that they try to learn at least one additional language sufficiently well to qualify as a translator ... but, this can be difficult.

