No Revolutionary War battles were waged in the State of New Hampshire. However, the state contributed several regiments which fought at Bunker Hill and many other battles. Famously, its citizen militia came to the aid of Vermonters to defend against the 1777 British invasion led by General John Burgoyne. The New Hampshire militia under the command of General John Stark thoroughly defeated and destroyed at the Battle of Bennington a contingent of Hessian soldiers sent by Burgoyne to gather horses and supplies.
Heald, Bruce D. New Hampshire and the Revolutionary War. Charleston, South Carolina: The History Press, 2013.
Society of Cincinatus, New Hampshire in the American Revolution: An Exhibit, http://societyofthecincinnati.org/pdf/downloads/exhibition_NewHampshire.pdf, 2010.