Norwich is a town in Windsor County , Vermont , United States , located along the Connecticut River opposite Hanover, New Hampshire . The population was 3,544 at the 2000 census. The name of the town was originally spelled "Norwhich", but the additional 'h' was dropped shortly after the town was chartered. The town was named after Norwich, Connecticut , the state from which the first settlers originated. Originally pronounced Norritch as per the English pronunciation ( Norwich, England ) the town name has in more recent times become more commonly pronounced Nor-wich . Norwich was the original home of Norwich University , which moved to Northfield in 1866 after a fire devastated the campus. Norwich is also the current home of the Montshire Museum of Science . Norwich maintains one of the few interstate public school systems, the Dresden School District , commissioned by President John F. Kennedy , which is shared by the towns of Norwich and Hanover, New Hampshire .