When were New England towns required to remove town government from their churches?

In the seventeenth and eighteenth centuries churches governed New England towns. At some time in the nineteenth century an authority, perhaps state, perhaps federal, passed a law (or made a judicial ruling) prohibiting that practice. When did this occur? Where can I read some of the details of this law (ruling)?

This should help:
http://en.wikipedia.org/wiki/Separation_of_church_and_state_in_the_United_States