N.H. Rev. Stat. Ann. § 457:2

No person shall marry his or her father, mother, father's brother, father's sister, mother's brother, mother's sister, son, daughter, brother, sister, son's son, son's daughter, daughter's son, daughter's daughter, brother's son, brother's daughter, sister's son, sister's daughter, father's brother's son, father's brother's daughter, mother's brother's son, mother's brother's daughter, father's sister's son, father's sister's daughter, mother's sister's son, or mother's sister's daughter. No person shall be allowed to be married to more than one person at any given time.