Conn. Gen. Stat. § 27-14: Governor to be commander-in-chief.

The Governor shall be the Captain-General and, as such, commander-in-chief of the militia, and of the National Guard and the naval militia, not in the service of the United States, and may employ it, or any part of it, for the defense or relief of the state or any part of its inhabitants or territory; and shall have all the powers necessary to carry into effect the provisions of this chapter. He shall issue all orders and prescribe all regulations for the organization and government of the organized militia, the National Guard and the naval militia. Such orders and regulations shall not be in conflict with the laws and regulations of the United States. He shall issue all orders and regulations necessary to cause the National Guard and naval militia to conform at all times to the laws and regulations of the United States relating thereto.