Adriaen Block, a Dutch sailor, was the first guy to touch down in the Nutmeg State. He sailed up the Connecticut River in 1614. The Dutch set up a fort in what is now Hartford. Massachusetts folks fed up with the Boston guys and the Puritans, started moving into the state in 1634. The Connecticut Colony was set up in 1639 (the ninth colony).
In 1638 Puritans set up the New Haven Colony along the coast. In 1662 the colony was granted a charter that went to the pacific coast. This is why you will find most Ohio records before the Revolution, and from the upper part of Pennsylvania sitting in boxes in the state house in Hartford. The colony grew rapidly during the 1600s. It became the fifth state in 1788.
After the Revolution, Connecticut became an industrial and factory state, and the population grew rapidly. General Israel Putnam retired to his farm in Brooklyn, Connecticut. I moved there in 1944, grew up there, and went to Yale in the late 1950s. It was odd growing up in Greenwich where Route 1 is Putnam Avenue, the main bank the Putnam Trust, and me spelling it Putman. Oh well.