Can you use drone over park? or is a permit needed? (Recreational use)

National Park Service does not permit drones over lands they manage

Policy Memorandum 14-05 (written June 2014) forbids the launching, landing, or operation of unmanned/remote control aircraft in national parks to include sandbars beaches water ways and open fields

I call the Park office and find out for sure

I would call and ask. There are a lot of state and federal laws involved with drone use and they'd know best.

This is best left to asking the park just to be safe. You may since it's a state park. But I can't be for sure.