Americans were divided on the English Civil War.

Puritan New Englanders supported the Puritan cause in England, not surprisingly. Many of them returned to England to fight for Cromwell. After the restoration, Massachusetts and New Haven harbored regicides who had fled from Charles II. A former governor of Massachusetts was also executed as a regicide under the restored monarchy.

Anglican Virginians, by contrast, supported the king, though not as actively as far as I can tell. They had problems closer to home, including a major Indian uprising and fighting next door in Maryland.

Maryland is the most complicated case. A battle took place there between Puritan settlers and the Catholic Lord Proprietor of the colony, Lord Baltimore.

For more information, I recommend The Cousin's Wars, by Kevin Phillips.