In New England Independents became Congregationalists. This means that though individual churches were "sufficient," meaning that they ran their affairs without intrusion from outside, they were also part of a network of mutual obligation and "watch care." Local churches regularly consulted each other on difficult questions about calling ministers or disciplining members — there was no such thing as a Congregational handbook that everyone could follow.
In 1648 the ministers of the Massachusetts Bay Colony met together to draw up the Cambridge Platform, a document that laid out standards for ordaining ministers, accepting new church members, and cooperation between local churches. This would be the closest Congregationalists would come to a constitution, and the last time they would all meet together for the next two centuries. Congregationalism in Connecticut took a slightly different tack: the Saybrook Platform of 1708 allowed for ministers to meet together in consociations and associations, and gave them power to make binding decisions over individual churches.
This Information is from the resources of the Congregational Library on Boston’s Beacon Hill. www.congregationallibrary.org