Connecticut was a self-governing, or charter, colony.
In effect, there were 3 types of American colonies. First, there were royal colonies, such as Virginia and Georgia. These colonies were under the authority of the English king.
Next, there were proprietary colonies, such as New Jersey, Pennsylvania, and Maryland. Proprietary colonies were large land grants from the English king to a proprietor or colonial governor. The governor was given governing rights over the colony he presided over. Of course, such a governor worked in close collaboration with the English court across the ocean.
The last type of colony was a self-governing/charter colony, which included Connecticut, Massachusetts, and Plymouth. Such a colony was also called a corporate colony in that the English king granted a charter to the citizens of the colony as a corporate body.
The Connecticut colony was originally founded by Thomas Hooker, a Newton minister in the Massachusetts colony. Historians maintain that Hooker looked towards Connecticut to escape the influence of John Cotton, the leading Puritan minister in Massachusetts.