The Office of Lieutenant Governor can be considered an entity in and of itself. Elected people serve in the role of Lieutenant Governor.
The following description is from the interactive Register and Manual on the Secretary of the State web site:
Before the Constitution of 1818, Connecticut had a Deputy Governor who presided in council, or the upper house of the General Assembly, in the absence of the Governor. When the Governor was present, the Deputy Governor had a voice in council. Until 1818 the Deputy Governor could exercise the office of a justice of the peace throughout the State, and could sign writs until 1879.
Today, the Lieutenant Governor is President of the State Senate, presides over its deliberations, rules on procedures, and may cast a vote in the event of a tie. The Lieutenant Governor may only enter debate when the State Senate meets as Committee of the Whole. Under the Constitution, the Lieutenant Governor becomes Governor in case of the death, resignation, refusal to serve or removal from office of the Governor. If the Governor is impeached or absent from the state, the Lieutenant Governor "shall exercise the powers and authority and perform the duties appertaining to the office of Governor until, if the Governor has been impeached, he is acquitted, or if absent, he has returned."
The Constitution also provides that the Lieutenant Governor shall exercise the powers and perform the duties of Governor if the Governor informs the Lieutenant Governor in writing that he is unable to do so, "until the Governor transmits to the Lieutenant Governor a written declaration to the contrary."
The Constitution also establishes procedures, under a Council on Gubernatorial Incapacity, whereby the Lieutenant Governor may assume the powers and duties of the Governor in the absence of a written declaration of incapacity by the Governor until it is determined that the Governor is able to resume the powers and duties of his office.
The Lieutenant Governor is a member of the Finance Advisory Committee, the Commission on Intergovernmental Cooperation and the Corporation of Yale University.
The Lieutenant Governor shall have the same qualifications for office as the Governor, is elected for four-year terms and receives an annual salary of $110,000.
See also entries under specific governor with whom they served.