Your city or town can take money off the property tax bill on your home if you are a veteran, or the spouse or surviving spouse of one. State law sets a standard credit amount and lets each municipality vote to adopt a larger one, so what you get depends on where you live. Separate credits cover wartime service, the surviving spouse of a wartime casualty, and total and permanent service-connected disability, and there is a full exemption for a home the VA helped you buy or adapt.
Contact the tax collector or assessing office in the city or town where your home is, because these credits are adopted and administered locally rather than by the state. The Department of Revenue Administration publishes which credits each municipality has adopted, and the New Hampshire Tax Collector Directory lists who to call.
Your DD214 or other discharge paperwork, your VA rating letter if you are claiming a disability credit, and proof you own and live in the home in New Hampshire.