If the county elections official finds that the copies of the petition are not signed by the requisite number of registered voters residing within the county he or she shall certify to the number of registered voters required to make the petition sufficient. Within 20 days from the date of that certificate, copies of the petition containing additional signatures secured either by the same persons theretofore appointed to secure signatures or by other persons appointed by the board of supervisors for that purpose may be filed with the county elections official.