Dorset is an unincorporated community in central Dorset Township, Ashtabula County, Ohio, United States. Although it is unincorporated, it has a post office, with the ZIP code of 44032. It lies along State Route 193.Dorset was originally named Millsford, and under the latter name was founded in 1828. The present name is after Dorset, Vermont, the native home of an early settler.