State law requires a health screening prior to entry (which may or may not specifically include vision, hearing, dental, or BMI exams).
New Hampshire Administrative Rules Ed 311.03 Physical Examination of Students
Schools shall accept documentation of a student's physical examination, provided:
(a) The examination has been performed within the past year; or
(b) If an examination has not been performed within the past year, the school shall accept documentation of an appointment for a physical examination with a licensed physician, advanced registered nurse practitioner or physician's assistant within a time determined by the school district for conditional enrollment.
New Hampshire Revised Statutes Annotated 200:32 Physical Examination of Pupils
There shall be a complete physical examination by a licensed physician, physician assistant, 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.