Within thirty (30) days after the date of issuance by the secretary of state of a certificate of organization of a soil conservation district, nominating petitions may be filed with the state soil conservation committee to nominate candidates for supervisors of the district. The committee shall have authority to extend the time within which nominating petitions may be filed. No nominating petition shall be accepted by the committee, unless it is subscribed to by twenty-five (25) or more owners of lands lying within the boundaries of such districts. Landowners may sign more than one (1) such nominating petition to nominate more than one (1) candidate for supervisor. The committee shall give due notice of an election to be held for the election of three (3) supervisors for the district. All owners of lands lying within the district shall be eligible to vote in the election. Only such landowners shall be eligible to vote. The three (3) candidates who receive the largest number, respectively, of the votes cast in the election shall be the elected supervisors for such district. The committee shall pay all the expenses of the election, shall supervise the conduct of the election, shall prescribe regulations governing the conduct of the election and the determination of the eligibility of voters in the election, and shall publish the results of the election.