Yes, handgun hunting is legal here in NH. If you handgun hunt in a rifle zone then basically any centerfire round is legal for deer. If you handgun hunt in an area where rifles are prohibited (shotgun/muzzleloader area) then you are limited to the following calibers - .357 Magnum, 10mm Auto, .41 Rem, .44 Magnum, .45 Long Colt, .480 Ruger or .500 Magnum. This area is the southeastern part of the state near the Mass border out to the seacoast. The rest of the state is mostly rifle anyway.