A new political party shall become eligible for recognition, shall be represented by an official party ballot at the next ensuing primary election of a county, city or town and shall be placed on the official ballot at the succeeding regular election on filing with the officer in charge of elections of the county or the city or town clerk, as the case may be, a petition signed by a number of qualified electors equal to not less than two percent of the votes cast for county attorney in the case of a county petition or for mayor in the case of a city or town petition. The county recorder or the city or town clerk, as applicable, shall review the petitions in the same manner prescribed by section 16-803, including the selection of a random sample of twenty percent of the total signatures eligible for verification, which shall be individually verified and certified, and shall perform a calculation and projection of the total number of valid signatures and make a determination whether the party shall be recognized as prescribed by section 16-803, subsection I.