The result of any election upon a proposed constitutional amendment or statute submitted or referred to the voters either by the Legislature or by initiative or referendum petition may be contested upon the petition of one or more registered voters directed against the Secretary of State. The petitioning voter or voters shall present a petition to the district court of Lancaster County within forty days after such election. The petition shall set forth the points on which the election will be contested and the facts which will be proved in support of such points and shall ask for leave to produce the proof. The Secretary of State shall be served with a copy of the petition and a notice of the time and place of the presentation of the petition ten days before the petition will be presented. The Secretary of State may, upon the presentation of such petition, file an answer thereto specifying reasons why the election should not be contested. The proponents and opponents of any proposed constitutional amendment or statute shall have the right to engage counsel to represent and act for such parties in all matters involved in and pertaining to the contest.