Upon the filing with the clerk of a municipality of the names of party-endorsed candidates pursuant to § 9-390 or upon the filing with such clerk of petitions for contesting candidates pursuant to § 9-412, such clerk shall verify and correct the names of any such candidate as the candidate authorizes the candidate’s name to appear on the ballot, pursuant to the certificate filed in accordance with subsection (c) of § 9-391 or the statement of consent filed in accordance with § 9-409, as applicable, endorse the same as having been so verified and corrected and use the same in the preparation of the ballots for the primary. The provisions of this section shall not apply to the municipal offices of state senator and state representative.