When was Connecticut annexed into the US?

Answer 1

Connecticut was not annexed to the United States.

This is a definitional issue. Annexation requires a larger complete entity passing a law or edict to absorb a smaller outside territorial entity. Connecticut was one of the original thirteen colonies/states and therefore was responsible for the creation of the United States. Since Connecticut created the United States (along with the other twelve colonies/states) it cannot be annexed by the United States.

The proper choice of words (and the answers) are either:

"When did Connecticut accept the Articles of Confederation and therefore joined the first form of the United States?" -- February 12, 1778 (It was the fifth of the thirteen colonies, since they were colonies at that point)

"When did Connecticut ratify the Constitution and therefore joined the United States as it now existed?" -- January 9, 1788 (It was the fifth of the thirteen states, since they were states at that point)

It is worth noting that it being the "fifth" both times is purely incidental.

Answer 2

January 9, 1788.