The statements provided for in section 16.1-15-41 must be certified by the members of the state canvassing board who shall subscribe their names to the statements. The board then shall determine what individuals have been duly elected to the offices, shall prepare and subscribe on each statement a certificate of that determination, and shall deliver the statement to the secretary of state. The candidate to be elected for each office receiving the highest number of votes must be duly elected to the office. An individual who was entitled to have the individual’s name appear on the primary election ballot, but whose name was not placed on the primary election ballot, may not be elected to a no-party office as a write-in candidate unless the individual receives a number of votes equal to or more than the number of signatures that would have been required to have the individual’s name placed on the primary election ballot.