Although the colonies were in their infancy, were they particularly in favor of one party in the Civil War? Did any fighting break out there? How aware were they of the troubles at home?
In Massachusetts, "the bias of the people was unfriendly to the King," though "divisions on the subject were taking place among the colonists".
Down south, "Virginia boasted that she was the last to acknowledge the authority of Cromwell and the first that returned her allegiance to the throne." Virginia had to be taken by force, after Charles' beheading and Cromwell's rise to power. A warship was sent to the port of Jamestown, though no shots were fired. (pp.35-41.) The Virginians surrendered amicably, terms of surrender were handed over for the colonial Assembly to sign, and the governor resigned. The terms were quite friendly to the colonists (free land, free trade, no taxes) and there was no further conflict between Virginia and Parliament. (pp.162-164.)
"Maryland was more disturbed than Virginia by the strife in England, becoming the scene of a fierce struggle for several years." Maryland's administration was pro-royal, but its citizenry was less so. Maryland was taken over by pro-Parliament forces in 1643-44, a period known as "the Plundering Time" due to rampant lawlessness. Order was restored, though more unrest broke out in 1649, culminating in the overthrow of the local government by ex-governor William Stone in 1655. This led to the Battle of the Severn in 1655, sometimes called the last battle of the English Civil War. Stone was defeated, and sentenced to death. He pled for mercy, which was granted, and he was not executed, though he died a few years later anyway. (1, 2, 3)
Rhode Island's position was more precarious than that of the other colonies, because they wanted to maintain their separation from the Massachusetts colony and continue offering religious freedom. Roger Williams was afraid they would lose their 1643 royal charter due to the change in leadership in England. Williams was friendly with several members of Parliament, and sailed for England in 1651 to plead his case. After speaking before Parliament and then talking directly to Oliver Cromwell, he was able to persuade the new government to allow Rhode Island to operate under its previous charter. He returned to Rhode Island in 1654, and Cromwell sent over a letter in 1655 upholding the original royal charter. No further strife with the Cromwell government occurred thereafter, as the Rhode Island citizenry was already rather anti-royal, or more to the point, anti-authoritarian. (1, 2, 3, 4)
The rest of the original Thirteen Colonies had not yet been established, or else were not yet under the control of the English.