Notwithstanding the provisions of any general statute to the contrary, in any town which provides for four-year terms for members to be elected to the board of education and whose legislative body adopts the provisions of this section by charter or ordinance, and the number of members to be elected is odd or even, any elector may vote for all of that number and the persons receiving the greatest number of votes shall be elected, except that when the number of members of any one political party who would be elected without regard to § 9-167a exceeds the maximum number as determined by said section, then only the candidates of such political party with the highest number of votes up to the limit of such maximum, shall be elected. The next highest ranking candidates, not from such political party, shall be elected, up to the number of places to be filled in such election. Each political party shall have the right to nominate as many persons as there are vacancies on the board and those names shall be placed upon the ballot.