Norwich is a village in Muskingum County, Ohio, United States. The population was 87 at the 2020 census. It is part of the Zanesville micropolitan area. Norwich was laid out in 1827, and named after Norwich, in England, the native home of a first settler. A post office has been in operation at Norwich since 1828. By 1833, Norwich had four stores, t…Norwich is a village in Muskingum County, Ohio, United States. The population was 87 at the 2020 census. It is part of the Zanesville micropolitan area. Norwich was laid out in 1827, and named after Norwich, in England, the native home of a first settler. A post office has been in operation at Norwich since 1828. By 1833, Norwich had four stores, two churches, and two taverns. The village was incorporated in 1833.