This is from the rules of Indiana State parks. You can legally carry a handgun at Turkey Run, and most (if not all) Indiana state parks. As singlestacksig stated above, Army Corp property does not allow carry.
"Any firearm (except lawfully possessed handguns),BB gun, air gun, CO2 gun, bow and arrow, paint gun or spear gun in possession in a state park must be unloaded or un-nocked and stored in a case or locked within a vehicle, except when owner is participating in an activity authorized by written permit."
Nope, you can conceal carry or open carry in the state park. Besides deer, raccoons, and woodpeckers (bastards are mean) you wont see much dangerous wild life.