At all special meetings of the District, the provisions of 17 V.S.A. chapter 51 regarding election officials (subchapter 1), voting machines (subchapter 3), polling places (subchapter 4), absent voters (subchapter 6), process of voting (subchapter 7), count and return of votes (subchapter 8), recounts and contest of elections (subchapter 9), and jurisdiction of courts (subchapter 10) shall apply except where clearly inapplicable. The District Secretary shall perform the functions assigned to the Secretary of State under chapter 51. The Chittenden Superior Court shall have jurisdiction over petitions for recounts. Election expenses shall be borne by the District.