Okay, I checked the revised statutes of the state of New Hampshire, 1842.
"No man shall marry his father's sister, mother's sister, father's widow, wife's mother, daughter, wife's daughter, son's widow, sister, son's daughter, daughter's daughter, son's son's widow, daughter's son's widow, brother's daughter or sister's daughter."
An Act to prevent Incestuous Marriages, 1791: "No woman shall marry her father's brother, mother's brother, mother's husband, husband's father, son, husband's son, daughter's husband, brother, son's son, daughter's son, son's daughter's husband, daughter's daughter's husband, brother's son, sister's son."
So there you have it. Avunculate marriages were illegal both before and after this time period in NH.