New York Consolidated Laws, Election Law - ELN § 15-134. Failure to designate terms

No election of village officers, held in any village, shall be invalid on account of the failure of the electors to designate in their ballots the respective terms of office of persons to be elected thereat, for the same office, for different terms;  but the persons so to be elected to such office, who are eligible and receive the highest number of votes, shall be elected.  The person first named on a ballot containing the names of more than one person for such an office, and not designating their respective terms, shall be deemed designated for the longest term, the second, for the next longest term, and so on to the end;  and the inspectors of election shall count the ballots and certify the result accordingly.