The government of the New Puritans in the country was strictly puritan and based on Theocracy at the time of the witch trials.
Explanation:
Salem Witch trails happened shortly after the settlement of the Puritans into new England area of the current USA which was a settlement made by the mostly catholic population to escape religious persecution back home in England.
As such they were very orthodox and very unrelenting when it came to matters like witchcraft and used a swimming test convince that the witches they had selected were indeed that.
Now it is a test that was deemed to fail and the autocracy must have known it anyway.