Good question - no, they don’t. Again, do all US States allow concealed carry? I would like to be able to do that here.
Most do, I believe. Either with or without permits. More and more of the states that allow concealed carry are moving to permitless carry, over the shrieks of the left.
In New Hampshire the right to carry a handgun either openly or concealed is not contingent on any government action. You can just go ahead and do it. (Assuming you are not a convicted felon, or a person otherwise not allowed to possess a firearm due to age, or other factors.)
There are some federal laws that apply to particular places however, such as Post Offices, schools, and airports.
There are also some regulations related to hunting, so if you are wandering around in the woods during hunting season with a gun and a dead dear on your ATV then you need to have a hunting license.
No, they don't, though most do.