N.H. Rev. Stat. Ann. § 610:1

The county commissioners of any county, the city council of a city and the selectmen of a town are authorized, whenever in their opinion the public good requires it, to offer and pay from the treasury of such county, city or town a suitable reward, not exceeding $300 in any one case, to any person who shall, in consequence of such offer, apprehend and secure any person or persons charged with having committed a capital or other high crime.