I looked through the FAQ and did a search with the terms "America English Civil War" and "Colonies English Civil War" and procured these threads that may interest you. There hasn't been quite so extensive an answer as I think this topic merits, but there's some good stuff to get started on.

• How did the British colonies react to the English Civil war, and what bearing did they have on the conflict? - The top level comment gives a good summary of how the English Civil War affected the colonies and the colonials' responses to Cromwell's rule.
• What happened to the New World colonies of England during the English Civil War? - One top level comment gives a good rundown of events in the colonies in relation to the war and gives a good source recommendation that directly addresses your question. They also have a variety of internet accessible citations that you may enjoy.
• What affect did the English Civil War (1642–1651) have on England's American colonies? - The larger of the two top level comments talks about the connection that the Founding Fathers' ancestors and politics had to the English Civil War that predated them, which is outside of the scope of your question but an interesting note in my opinion.

There is also a Wikipedia article entitled "English overseas possessions in the Wars of the Three Kingdoms" which has sections devoted to the Chesapeake Colonies and the Northern Colonies along with a decent references section that cites many internet accessible sources as well as a few books that may be of interest.