Norwich is a town in Windsor County, in the U.S. state of Vermont. The population was 3,414 at the 2010 census. Home to some of the state of Vermont's wealthiest residents, the municipality is a commuter town for nearby Hanover, New Hampshire across the Connecticut River. The town is part of the Dresden School District, the first interstate school district in the United States, signed into law by President John F. Kennedy. The town contains the Norwich Mid-Century Modern Historic District.