There is no law preventing you from carrying in a state park or forest.
The only state restrictions on where you can carry are schools and wherever the state legislature is meeting.
With that said, there are environmental laws that say that if you are carrying a gun, and it is not a gun legal for hunting whatever is in season, and you don't have the proper permits and tags, then it is prima facia evidence of poaching.
Realistically, here is how it works according to a CT conservation officer I spoke with on this topic.
If you are going hunting, lets say deer hunting with a muzzle loader or bow, you had better leave that .22 revolver at home. It could be construed that you are poaching with the revolver.
If you are out hiking, dressed in hiking clothes, making noise, you have nothing to worry about, because you are clearly not "hunting".
Hope this helps.
Bottom line is that if you are out hunting, don't bring a handgun as a "backup" or as "protection". If you are out enjoying a day in the woods, then carry as you would like.