In the 1640s, England fell into Civil War over the rule of Charles I. After much conflict, Charles was executed in January 1649. Oliver Cromwell took over, essentially pushing England into a military dictatorship. The monarchy was restored in May 1660, with Charles II.
The Wars impacted Connecticut in two ways. First, some of those who had signed the death warrant of Charles I fled to New Haven after the Restoration, hiding out for fear of execution. The Colony hid them. Second and more importantly, they resulted in Connecticut receiving a royal charter for the first time. That charter, among other innovations, absorbed New Haven Colony into Connecticut Colony.
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Connecticut Roots by Charter Oak Genealogy 