Yes you are.
Federal law, thanks Obama, says federal parks have to follow State law. So yes, you are good to go in a federal park if you are good in that state.
http://www.nps.gov/appa/learn/management/questions-and-answers.htm
State parks follow state law. And some states that allow ccw do not allow in state parks, but not very many. Most changed that law after Obama signed the federal law.