N.H. Rev. Stat. Ann. § 193:5

Whenever it shall appear to the superintendent of schools that the welfare of any child will be best served by the withdrawal of such child from school, the superintendent or a majority of the members of the school board shall make recommendation to the commissioner of education, who shall, if the facts warrant it, make an order exempting such child from attendance for such period of time as seems best for the interest of such child.