Upon receipt of the order from the supreme court, the secretary of state shall issue a recall petition. When the required number of signatures on the petition have been secured, the petition may be filed with the secretary of state. The petition must be filed within 90 days after the date of issuance. Upon the filing of the petition, the secretary of state shall verify the number and eligibility of signers in the manner provided by the secretary of state. If the secretary of state determines that a petition has been signed by a sufficient number of eligible voters, the secretary of state shall certify the petition and immediately notify in writing the governor, the petitioners, and the state officer named in the petition. If the petition is not signed by a sufficient number of eligible voters, the secretary of state shall dismiss the petition.