Norman is an unincorporated town in northwestern Owen Township, Jackson County, Indiana, United States. It lies along State Road 58 northwest of Brownstown, the county seat of Jackson County. Because the community had two different names, the Board on Geographic Names officially decided in favor of "Norman" in 1943. It has a post office, wit…Norman is an unincorporated town in northwestern Owen Township, Jackson County, Indiana, United States. It lies along State Road 58 northwest of Brownstown, the county seat of Jackson County. Because the community had two different names, the Board on Geographic Names officially decided in favor of "Norman" in 1943. It has a post office, with the ZIP code of 47264.