Thank you for your response. How would I go about finding non-civil service department that are hiring such positions?Make sure you take the Civil Service Exam. If you don't, you won't get another shot for two years. You'll regret it until 2007.
If you're applying to non civil service towns, they usually move pretty quick, so you'll want to apply about a month before graduation. If you could start working a part time Police job, or a dispatch position, it could help a lot. A lot of departments like to hire from within.