N.H. Rev. Stat. Ann. § 200:32

There shall be a complete physical examination by a licensed physician, physician associate, or advanced practice registered nurse of each child prior to or upon first entry into the public school system and thereafter as often as deemed necessary by the local school authority. The result of the child's physical examination shall be presented to the local school officials on a form provided by the local school authorities. No physical examination shall be required of a child whose parent or guardian objects thereto in writing on the grounds that such physical examination is contrary to the child's religious tenets and teachings.