The delegates to the state convention of each party elected from each town shall select a chairman of such delegation and file the name and address of such chairman with the secretary of the state central committee of such party prior to the opening of such convention. Whenever one-fifth or more of the accredited delegates to, and present and voting at, any such state convention called for the purpose of choosing candidates for nomination for any elective office, upon motion, vote that a roll call vote, under § 9-385, upon any matter or motion pending before such convention, or on a party endorsement as between two or more candidates for nomination to any state office at any such convention, be taken by town delegation, the individual delegates shall be polled by the chairman of each town delegation whose designation is recorded as provided herein and their votes cast by totals by such chairman on the roll call. A list of the names and the vote of each delegate shall be filed by the said chairman of each town delegation with the clerk or secretary of the convention prior to the announcement of the result of such roll call vote and shall be preserved with the record of the vote as provided in § 9-385. A duplicate copy of such list shall be filed with the Secretary of the State not later than forty-eight hours after the close of such convention. Upon announcement by the chairman of the vote of a town delegation, any delegate from such town may question or challenge such announcement, and thereupon, the vote of such town delegation shall be individually taken by the clerk or the secretary of such convention calling the roll, and each delegate shall announce his own vote. The provisions of this law shall not apply to district delegates, if any, and district delegates shall continue to vote individually on any roll call.