If the county elections official, by his or her certificate, finds that a petition is insufficient, he or she shall certify to the number of additional signatures of qualified electors required to make the petition sufficient, and the petition may be amended by a supplemental petition filed within 10 days from the date of the certificate. Within 10 days after a supplemental petition has been filed, the county elections official shall examine it and certify to the result of the examination. If this certificate shows the petition as amended to be insufficient, it shall be filed by the county elections official in his or her office and kept as a public record, without prejudice to the filing of any other petition to the same effect not less than six months thereafter. If the certificate shows the petition or petition as amended to be sufficient, the county elections official shall present it to the board of supervisors without delay with his or her certificate attached and properly dated.