Barnett is a city in Morgan County, Missouri, United States. The population was 158 at the 2020 census, down from 203 in 2010. Variant names …Barnett is a city in Morgan County, Missouri, United States. The population was 158 at the 2020 census, down from 203 in 2010. Variant names were "Stone House" and "Barnetsville". A post office called Stone House was established in 1858, and the name was changed to Barnetsville in 1875. For a brief period of time, the name was Marysville, after a citizen named Mary Justice. The name changed to Barnett in 1880, when the town was rebuilt following a tornado. The present name is after one Mr. Barnet, an early settler.
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