Rather than answer to a different principal in each school, the Special Tutor is responsible only to the superintendent of the entire district.
Rather than answer to a different principal in each school, the Special Tutor is responsible only under the superintendent of the entire district.
Rather than answer to a different principal in each school, the Special Tutor is responsible only to the superintendent of the entire district.
Rather than answer to a different principal in each school, the Special Tutor is responsible only under the superintendent of the entire district.
In discussing the authority figure whom somebody serves, the correct idiom is "responsible to [the authority figure]." The word "responsible" takes only two prepositions: "for" an issue, and "to" an authority figure.