I'm sure that came back with a proud New Hampshire veteran. There are actually lots of American Civil War relics to be found at period homesites all over the country, and in places never having seen any military action at all. That war was pervasive. Every home sent somebody to the war, and if they came back alive, they probably brought back a uniform with a belt, and some buttons. Maybe even a surplus rifle!
Great find! Many a man (overgrown boy) dreams of finding one of those!