Elizabeth is a town in Posey Township, Harrison County, Indiana, United States. The population was 162 at the 2010 census. The original plat of the town of Elizabeth was recorded on April 17, 1812. It was witnessed by Sheriff John Tipton. The land for the town was donated by Capt. Jacob Zenor and wife Suzannah Muchendorffer Zenor. The town is named …Elizabeth is a town in Posey Township, Harrison County, Indiana, United States. The population was 162 at the 2010 census. The original plat of the town of Elizabeth was recorded on April 17, 1812. It was witnessed by Sheriff John Tipton. The land for the town was donated by Capt. Jacob Zenor and wife Suzannah Muchendorffer Zenor. The town is named after Jacob's daughter-in-law Elizabeth Lemmon Zenor wife of George Zenor.