The maximum length of stay at most state parks is 14 days before you have to leave for at least 48 hours before you can return again to the same state park.
However all state parks can have their own regulations and rules on the length of stay.
Most people though stay at state parks for no longer than 7 days at a time anyway but it's usually okay for you to stay at a state park for 14 days at most before you have to leave.
So if you want to stay at a state park for a month then you would need to leave after 14 days and stay away for at least 2 days.
Then you could come back and stay again another 14 days and then leave.
This is how I did it before when I went to a lovely state park I wanted to stay a month at but could only stay for 14 days at a time.
I left after 14 days and then went and stayed somewhere else for a few days and then later after those 2 days I returned to the stay park again for the other 2 weeks.