Norwichis a town inWindsor County, Vermont, in the United States.The landscape is hilly and wooded.Home to some of the state ofVermont's wealthiest residents, the municipality is acommuter townfor nearbyHanover, New Hampshireacross theConnecticut River. The town is part of theDresden School District, the firstinterstate school districtin theUnited States, signed into law by PresidentJohn F. Kennedy.