According strictly to the FAA. However, state and federal government control airspace above their borders. Federal parks, for example, are illegal to fly. It’s tough to get permission, I live 5 miles from Great Smoky Mountain National Park.
Two buildings, side by side want a bridge between the two on the 20th floor for convenience. Had to buy the airspace from the state.
Ahh, from what I have read about this subject, you can fly over NPs you just can't take off or land in them. Plus you cannot 'harass' the wildlife. If you take off & land outside many types of parks, you are not breaking any laws. Check it out on of the many links on DJI:
Filming National Parks From Outside