In the case of a primary for state or district office, each person certified by the Secretary of the State as provided in § 9-440, to have received the greatest number of votes of the electors eligible to vote in a primary for any office shall be deemed to have been chosen as the nominee of such party to such office. In the case of a primary for a municipal office, the moderator, or the head moderator, as the case may be, shall declare nominated the person having the greatest number of votes for such office and, if more than one person is to be nominated for the same office, he shall declare nominated the persons having the greatest number of votes for such office up to the number to be chosen. In the case of a primary for members of a town committee, such moderator shall declare elected the persons having the greatest number of votes for such positions up to the number to be chosen for such positions. In the case of a primary for justice of the peace, such moderator shall declare elected each person on the slate having the greatest number of votes for such offices. In all primaries, a plurality of the votes cast shall be sufficient to nominate or elect, as the case may be.