(a) (1) Any county adjacent to a district maintaining a district health department may, with the approval of the State Board of Health, become a part of the district by either of the following two (2) methods:

(A) By agreement between the county courts of the counties comprising the district;

(B) By a petition signed by one hundred (100) or more of the qualified electors of the county presented to the county court of the county. The court shall thereupon, by an order, direct the clerk of the county to certify to the county board of election commissioners the proposition to be submitted to the electors of the county at the next general election, and, in the event that a majority vote in favor of the proposition, the county shall thereupon be added to the district.

(2) Upon being accepted into a district, a county shall thereupon become subject to all of the provisions of this act as though it were originally a part of the district.

(b) Any municipal corporation which has voluntarily merged its health department with a county or district health department, under the authority of § 14-262-107, may withdraw from the county or district health department by resolution of its city council, board of trustees, or other governing body; however, no municipal corporation may withdraw from a department within the two-year period following the municipal corporation's becoming a part of the department, and then only after ninety (90) days' written notice given to the department.

(c) Any county which has become a part of a district health department may withdraw from the district health department pursuant to the following procedure: Upon a petition of one hundred (100) or more qualified electors, the county court shall, by an order, direct the county clerk to certify to the county board of election commissioners the question of withdrawal, which shall be submitted to the electors of the county at the next general election; in the event the vote is favorable to the withdrawal, the county court shall thereupon formally withdraw the county from the district health department, but only after ninety (90) days' written notice is given to the district health department, and the withdrawal may not be less than two (2) years after the entry of the county into the district health department.