If the requisite number of county officers are not elected because two or more persons have equal and the highest number of votes for one and the same office, a recount must be done pursuant to section 16.1-16-01. If a recount results in a tie vote, the county auditor shall give notice to the persons to appear at the county auditor’s office at a time appointed by the county auditor. The persons then shall publicly decide by a drawing of names which of them must be declared elected. The county auditor shall prepare and deliver to the person elected an election certificate as provided in this chapter.