If the electors fail to choose a candidate for any office by reason of an equality of votes at any election, and no provision is otherwise made by law for the election of a candidate to such office, such election shall stand adjourned for three weeks at the same hour at which the first election was held. Ballots of the same form and description as described in sections 9-250 to 9-256, inclusive, except that such ballots shall contain only the names of the candidates for whom the same are to be voted, shall be used in the election on such adjourned day, and the election shall be conducted in the same manner as on the first day, except that the votes shall be cast for such officer only. Ballots for such election shall be provided forthwith by the clerk of the municipality wherein such election stands adjourned, and such clerk shall furnish the Secretary of the State with an accurate list of all candidates to be voted for at such adjourned election. The clerk of the municipality wherein such election so stands adjourned shall, at least three days prior to the day of such adjourned election, give notice of the day, hours, place and purpose thereof by publishing such notice in a newspaper published in such municipality or having a circulation therein. No such election shall be held if prior to such election all but one of the candidates for such office die, withdraw their names or for any reason become disqualified to hold such office, and, in such event, the remaining candidate shall be deemed to be lawfully elected to such office. No withdrawal shall be valid until the candidate who has withdrawn has filed a letter of withdrawal signed by such candidate with the Secretary of the State or, in the case of a municipal office, until the candidate who has withdrawn has filed a letter of withdrawal signed by such candidate with the municipal clerk. When such an election is required to be held under the provisions of this section for any office other than a municipal office, and prior to such election all but one of the candidates for such office die, withdraw their names or for any reason become disqualified to hold such office, the Secretary of the State shall forthwith notify the clerk of each municipality wherein such election was to have been held of such fact, and shall forthwith direct each such clerk that such election shall not be held. In the case of a multiple opening office only the names of those candidates whose votes are equal shall be placed on the ballot of the adjourned election.