The first formal government of Connecticut was set forth by The Fundamental Orders, adopted on January 14, 1639 OS (January 24 NS). (You can read the text here.) It has the features of a written constitution, and is considered by some as the first written Constitution in the Western tradition, thus earning Connecticut its nickname of The Constitution State.
In 1660, King Charles II reassumed the monarchy in England, effectively ending the period of the English Revolution. (The English Civil War led to the trial and execution of Charles I, the exile of his son, Charles II, and replacement of English monarchy with, first, the Commonwealth of England (1649–53), and then with a Protectorate (1653–59) under Oliver Cromwell’s personal rule.) Since Connecticut had never been officially recognized as a colony by the crown, the General Court determined that the independence of Connecticut must be legitimized. Connecticut’s governor, John Winthrop, Jr., was sent as an emissary to negotiate with the English government, and set sail for England on July 23, 1661. He proved successful in his mission, and the English attorney general approved a bill for incorporation of the Connecticut Charter. After being officially sealed and registered, the document was returned to Connecticut and adopted by the General Court on October 9, 1662. (You can read the text here.)
The Connecticut Charter displaced the Fundamental Orders to become the governing authority for the colony. Its practical effect on the government however, was minimal and Connecticut continued to operate much as it had under the Fundamental Orders.
The General Assembly formally approved the Declaration of Independence with the other colonies. However, in its resolution the legislature it declared that Connecticut’s government, “shall continue to be as established by Charter received from Charles the second, King of England, so far as an adherence to the same will be consistent with an absolute independence of this State on the Crown of Great Britain…” While eleven of the thirteen colonies had drafted state constitutions by 1786, Connecticut elected to continue operation under the Charter. Connecticut retained this scheme of government until 1818, when the first true constitution was adopted.
As a result of the 1818 constitution, the Congregational Church was finally disestablished. (You can read the text of that constitution here.)
(In 1801, Danbury, Connecticut Baptists sent a letter to President Thomas Jefferson complaining that, in their state, the religious liberties they enjoyed were not seen as immutable rights, but as privileges granted by the legislature — as “favors granted.” Jefferson responded, in part:
Believing with you that religion is a matter which lies solely between Man & his God, that he owes account to none other for his faith or his worship, that the legitimate powers of government reach actions only, & not opinions, I contemplate with sovereign reverence that act of the whole American people which declared that their legislature should “make no law respecting an establishment of religion, or prohibiting the free exercise thereof,” thus building a wall of separation between Church & State.”
[His reply did not address their concerns about problems with state establishment of religion — only of establishment on the national level.] The letter is however most famous for its use of the phrase “wall of separation between church and state,” which led to the Establishment Clause that we use today. You can read Jefferson’s entire letter here.
In other matters, the 1818 Constitution solidified new voting rights, and separation of powers was finally brought to Connecticut government. An independent judiciary was approved.
The constitution did not significantly change the role of the executive, and the branch remained relatively weak. The executive did however, became a constitutional and independent part of the government.
The legislative branch also experienced a few changes. The Council was renamed the Senate. By constitutional mandate, half the legislative sessions were to take place in Hartford with the other half convening in New Haven.
Although many amendments were added over the years, the Constitution of 1818 remained in operation until 1965. There was also a Constitution of 1955, but it merely incorporated prior amendments into the main body of the constitution.
Connecticut currently operates under the constitution passed in 1965, the text of which is here. The primary purpose of the 1965 constitutional convention was reapportionment of the representatives in the lower legislative house. Apart from this major change, a majority of the language from the 1818 Constitution was reaffirmed verbatim or almost verbatim in 1965. The Constitution of 1965 remains the supreme authority in Connecticut today, although it has been amended quite a few times. You can access a legislative history of amendments here.