(A) For purposes of this section:

(1) “Carryover property” has the same meaning as in section 319.301 of the Revised Code.

(2) “Residential/agricultural real property” has the same meaning as in section 5705.219 of the Revised Code.

(B) For each city, local, or exempted village school district in which the tax authorized by section 5705.219 of the Revised Code has been approved by electors in the preceding year, the tax commissioner, not later than the twenty-eighth day of February, shall certify to the department of education the amount determined in division (B)(4) of section 5705.219 of the Revised Code. Not later than the twenty-eighth day of February of each year thereafter for twelve years, the commissioner shall certify an amount equal to the difference between the amount certified in the preceding year under this division and the product of ten mills per dollar multiplied by the excess, if any, of the value of carryover property for residential/agricultural real property for the preceding tax year over the value of carryover property for residential/agricultural real property in the second preceding tax year. If the amount to be certified in any year is zero, in the commissioner’s certification the commissioner shall state that no further certifications shall be forthcoming.

(C) Not later than the last day of April and of October beginning in the first year in which a certification under division (B) of this section is received, the department of education shall pay to the school district for which the certification is made one-half of the amount most recently certified by the tax commissioner.