Mirroring the above, it really depend on what SPECIFIC job duties you anticipate. Personally, I think an AA or AS is basically useless, only usually sought (or requirements met) as a way to get the core courses out of the way for a BA or BS. If you're going to be investigating financial crimes or fraud, for example, a degree in accounting or finance will be much more useful and thus desirable. Joining ACFE (Association of Certified Fraud Examiners) as a student member or even just browsing their website might be helpful to get actual commentary from those within the field. They have multiple "routes" to accumulating the training and experience needed for certification, and these various skill trees mirror what public and private employers are seeking.
Similarly, if you want to work in crime analysis, join the International Association of Crime Analysts as a student member, and you'll get access to the very rare and specific job opportunities nationwide - read carefully what SPECIFIC skills are being sought, and structure your degree accordingly.
ACFE is also well known for having student mentors as well as local monthly chapter meetings, whereas IACA is known for having only a single big annual nationwide event. Having been a member of both groups, I can't stress how important it is to make the most of their websites and when possible, attending gatherings and trainings (even if you don't seek their certifications - you can always position yourself for employment first, and then let your employer pay for the certifications).
Having worked in positions as varied as 911 operator, victim advocate, analyst, and auditor within the CJ system, it's MOST important to have a well rounded background (ie really applicable electives or even certificates/certifications) in ADDITION to just the base degree; criminal justice or otherwise. Most CJ degrees give very broad strokes (and really, when working a crime scene, do the credits in corrections required for the degree help you? No.) and it's the student who chooses to supplement the basics with specifics who end up with the edge.
For me personally, my CJ degree wasn't that helpful - again, because the course material is SO broad (admin stuff, corrections, patrol configurations) - it's always been computer, research, and database manipulation sklls that have been my personal steps up, and obviously, due to the nature of the beast, one's report writing ability can make or break you. Even if not required for the degree, in almost any position within CJ, where you're a potential official statement looking for a place to happen, or the next witness to take the stand, one's spelling, grammar, and ability to communicate are often under appreciated yet incredibly vital to success within the field.

