In a book titled America's Providential History it states on page 84 that
The major Puritan weakness was their holding to the idea of a State Church. They saw nothing wrong with a National church.
But it doesn't give any evidence. I personally don't think that they would want a State Church, since they knew that England's church had started out good and eventually became rotten (in their minds). Is there any evidence out there that supports this idea?