The State Board of Education may examine any incorporated or endowed high school or academy in this state and, if it appears that such school or academy meets the requirements of the State Board of Education for the approval of public high schools, said board may approve such school or academy under the provisions of this part, and any town in which a high school is not maintained shall pay the whole of the tuition fees of pupils attending such school or academy, except if it is a school under ecclesiastical control.