(a) Any charter adopted or amended under the provisions of this chapter shall conform to the following requirements:

(1) The municipality shall have a legislative body, which may be: (A) A town meeting; (B) a representative town meeting; (C) a board of selectmen, council, board of directors, board of aldermen or board of burgesses; or (D) a combination of a town meeting or representative town meeting and one of the bodies listed in subparagraph (C). In any combination, the body having the greater number of members shall have the power to adopt the annual budget and shall have such other powers as the charter prescribes, and the body having the lesser number of members shall have the power to adopt, amend and repeal ordinances, subject to any limitations imposed by the general statutes or by the charter. The number of members in any elective legislative body, the terms of office of such members and the method by which they are elected shall be prescribed by the charter.

(2) The municipality shall have a chief executive officer, who may be one of the following: (A) The first selectman; (B) a chief administrative officer appointed by the board of selectmen; (C) a mayor elected by the electors of the municipality; (D) a warden elected by the electors of the borough; (E) a town, city or borough manager appointed by the board of selectmen, the council, the board of directors, the board of aldermen or the board of burgesses; (F) a chief administrative officer appointed by the mayor. Any municipality having a manager as its chief executive officer may also have a mayor who shall be the presiding officer of its legislative body, shall be the ceremonial head of such municipality and shall have such other powers and duties as the charter prescribes. The powers, duties and term of office of the chief executive officer shall be those prescribed by the general statutes and he shall have such other powers and duties as the charter prescribes.

(b) Every municipality shall have all municipal officers, departments, boards, commissions and agencies which are required by the general statutes or by the charter. Each municipality may have any municipal officers, departments, boards, commissions and agencies which are specifically allowed by the general statutes or which are necessary to carry out any municipal powers, duties or responsibilities under the general statutes. All such officers, departments, boards, commissions and agencies shall be elected, appointed and organized in the manner provided by the general statutes, except as otherwise provided by the charter or by ordinances or resolutions adopted pursuant to such charter. Any municipality may, by charter or by ordinances or resolutions adopted pursuant to such charter, alter the method of election, appointment or organization of any or all of such officers, departments, boards, commissions or agencies, including combining or separating the duties of each, unless specifically prohibited from making such alteration by the Constitution or the general statutes.