I have to agree with some of the stuff stated previously.
I would definitely contact your local Parks and Recreation Dept. and see if they have a policy concerning geocaching.
If they do have a policy in place and you place a cache without permission I'm sure they would take some sort of action. That could be anything from a fine to a ticket. It would be bad if they found a cache that was not registered and assumed the worst and called the police to handle it. Something like that could possibly jeopardize geocaching in all of that system's parks.
My $.02 worth