The state or county executive committee of any political party may, by a majority vote of the committee, require that members of the committee be elected by the qualified electors of such political party. If such committee adopts an appropriate resolution requiring that such members be so elected, such election shall be held on the same ballot as the gubernatorial primary election. When members of county or state executive committees are to be elected in a primary, their declarations of candidacy shall be filed in the same manner and within the same time as candidates for nomination for public office.