N.H. Rev. Stat. Ann. § 166:24

If a county acting in its capacity as agent for a city or town under RSA 165:34 spends any sum for the support, return to his home or burial of a county assisted person having a residence in a town or city, or another county, or for the support, return to his home or burial of an assisted person having relations able to support him under RSA 165:19, such sum may be recovered from the town, city, county or relation so chargeable. In any civil action brought under this section to recover such sum, the court shall award costs to the prevailing party.