N.H. Rev. Stat. Ann. § 263:37

Whenever a motor vehicle of a nonresident may be driven on the ways of this state, without registration, or is driven under a neutral zone registration, such vehicle may be driven by its owner or by his employee without a license from the director if the driver is duly licensed under the laws of the state, district, or country in which the motor vehicle is registered, or has complied fully with the laws of the state where said motor vehicle is registered respecting the licensing of motor vehicle drivers; provided, that said state, district, or country grants like privileges to residents of this state.