Any district shall pay for the tuition of any pupil who, as a resident of the district, has been assigned to attend a public elementary or junior high school or school of corresponding grade in another district or a private school approved as a school tuition program by the school board pursuant to N.H. Rev. Stat. § 193:3, VII, and any district not maintaining an elementary or junior high school or school of corresponding grade shall pay for the tuition of any pupil who, as a resident of the district, is determined to be entitled to have such tuition paid by the district where the pupil resides, and who attends an approved public elementary or junior high school or public school of corresponding grade in another district, or a private school approved as a school tuition program by the school board pursuant to N.H. Rev. Stat. § 193:3, VII. Except under contract, the liability of any school district under this section for the tuition of any pupil shall be the current expenses of operation of the receiving district for its elementary or junior high school or public school of corresponding grade, as estimated by the state board of education for the preceding school year. This current expense of operation shall include all costs except costs of transportation of pupils.