(A) Notwithstanding any provision of the Revised Code to the contrary, for the purpose of nominating candidates for a position as a member of the board of education of a city, local, or exempted village school district or a position as a member of a governing board of an educational service center, the board may adopt, by resolution upon a three-fifths majority vote of its total membership, procedures for a nonpartisan primary election. Such procedures shall specify the following:

1. (1) That the primary election for nominating candidates for a position as a member of that board shall be held on the same day as the primary election for nominating all other candidates for public office in that year;
2. (2) That nominating petitions shall be filed with the board of elections not later than four p.m. of the ninetieth day before the day of the primary election;
3. (3) That the primary election shall take place only if the number of candidates for nomination for a position on that board, as verified by the board of elections, is at least one more than two times the number of available positions on that board at the general election;
4. (4) That the number of candidates advancing from the primary election to the general election shall equal two times the number of available positions on that board at the general election. The board shall notify the board of elections upon adoption of a resolution under this division. No such resolution shall apply for a particular election unless the resolution is adopted at least one hundred twenty days prior to the deadline specified in the resolution to become a candidate for nomination at that election. Subject to division (B) of this section, the resolution shall apply to all subsequent nominations for a position as a member of that board.