Perhaps not if the park has its own jurisdiction - ie. It is its own municipality, not just a workplace or venue. The next handoff might be to the county, then to the state.
With such a large, well-funded park in such a remote area, that might be quite plausible.
And sometimes there are screw ups. West Yellowstone National Park has a section where nobody has jurisdiction to hold a trial as guaranteed by the Constitution's 6th Amendment, which reads:
The catch with west Yellowstone is that the district is in a different judicial district than the actual state, just to simplify things, so it's impossible to have a trial in the state and district wherein the crime was committed. That area also doesn't have enough residents to impound a jury.