A bit of follow-up history -- the New England Theocracy was destroyed after the Witch Trials, and religious and secular authority became separated. This separation was of the utmost importance. Two generations later, when the Framers of the Constitution began designing a new method of government, the concept of separating Church and State was utmost in their minds, not only from knowing their own country's history, regarding what happened in New England, but also knowing the bloody history of "Old" England during its religious conflicts between Protestant and Catholic. If anything good came out of the Witch Hysteria of the 1690's, it was this separation of authority, which thankfully has remained mostly intact in the United States.
The Puritans lived in a theocracy, a government based on religion in which God is the ultimate authority. The laws of the church are the same as the laws of society. Hester must face the ruling of the church elders, Reverend Wilson and Reverend Dimmesdale, as well as Governor Bellingham. The "Puritanic code of law," as Hawthorne notes in Chapter 2, was harsh and severe with laws and rules stemming from religious law such as the Ten Commandments. Puritans had no separation of church and state as the Constitution guarantees today. The two were the same.