We visited the State House on June 20th. I did not find free parking around the State House. We had to park in a parking garage. When you finished the security check, go to the visitor's bureau. There you can get a self guiding booklet of the house and the grounds.
In every state that we visit we always visit the State House. This one is on the inside very beautiful.
If the House of Representatives is in session you can only view it from the balcony. Then you can see the Mace in front of the tribune. In the Senate you will see the Sword.