What was the structure of the government of Salem Town, Massachusetts in 1692?
Massachusetts’ government was in turmoil at the time, because the original charter under which the colony was settled was declared void (“vacated”) eight years earlier. Then the Glorious Revolution in 1689 replaced the Catholic James II with William and Mary, which had the effect of throwing out the then-Royal Governor of the colony. The previous one came back, but had no legal authority for this, siunce no action naming a replacement was around. More than one writer about the witch hysteria has claimed that this uncertainty contributed to the mood.
I know it’s not what you asked, but it’s the first thing that sprang to mind when I read your question, and it’s certainly relevant.
I don’t know what the town government of Salem Town or Salem Village were. To tell the truth, although I’ve read several books on the trials, I don’t recall anyone describing the precise form of government, whether mayor or town council or what. But it certainly wasn;t a theocracy. The trials were carried out by secular courts of Oyer and Terminer.The judges were not religioous leaders. Desp[ite what some people think, Cotton Mather never had any authority over these, and was only tangentially involved (although he wrote quite a bit about them).
Wikipedia has a good quick overview.