Hiring isn't that good. The only department that I know of that doesn't have a hiring freeze (in my area) is Detroit. But it looks like even Detroit is going to reinstate their hiring freeze, and possible (hopefully not) lay off their last graduating class. Luckily for you, you already have time on the job, so if you start faxing/emailing, your resume out now, to the departments your interested in, it will be on file, and you will get a call when an opening becomes available. It will at least get you an interview. The only chance most have of getting on a department right now is if you have years already on the job, a very high degree not only in CJ but also something like psychology, or if you have spend years (with good reviews) in the explorers, and cadets (with a low degree in CJ).
BTW, do yourself a favor and don't goto LPD. Try the multiple Sheriff's Departments first, they have less of a turn over, and better job security.