Unfortunately, possession, sale, import, and take (harm, harass, injuring, killing) of Eastern Box turtles is illegal in New Hampshire. You should take him back to the EXACT spot where you found him, or, turn him over to a licensed wildlife rehabilitation center.
Maybe you could get a license/permit to own him. I renew mine every year...I'm in NY. Box turtles are wonderful little pets if given the proper environment. While you have him make sure he is kept in a warm, humid enclosure, with plenty of places to dig under and hide...enough water to sit in, but not too deep. What ever you do...good luck.
A boxie that small, I would keep inside, in a planted vivarium. I have a three toed hatchling, and won't put him outside until next Spring, and if then, he would be in a small enclosure under my supervision, and not for too long. Eastern Box Turtles are native here, and at that age just hide under leaf litter and eat any small buggie thing they find under there. I feed hatchlings pill bugs, cut up worms and an occasional meal worm or wax worm. If you do keep him, make sure you put in plenty of leaf litter for him to dig under and hide....NO bright lights....moist, warm and humid. Something that small will dehydrate and die very fast. Also hatchlings are not easy to care for if you aren't experienced. Let us know what you do about this little guy.
But I'm with Kristina...he should go back exactly where you found him.