Jay,
I'm not certain, but It's likely that, unless you are appointed, there is a "merit system" in your local government that essentially gives you property rights to your job once you've passed the probationary period. Yes, it can be a bit of a nail biting experience getting through probation, but due to the nature of government (top level management being voted in or out every four years) there are protections to keep the system running by making it impossible to "be let go with no reason given." Essential public services would come to a complete halt if all the experienced people were let go whenever a new regime was put into place.
Of course that doesn't mean you can't be fired, especially if a law has been broken, but it does mean there are a great deal of steps that must be followed. (1)Verbal warning (2)1st Written Warning with corrective action plan, (3) 2nd Written Warning with new probationary period. Etc.
Do a good job, serve the public proudly and kiss the correct ass and you should do fine!
Best of luck.