Madison is an unincorporated community and census-designated place in Dorchester County, Maryland, United States. The population was 204 at the 2010 census. In the early 19th century, the community was a hamlet known as "Tobacco Stick." Around 1822, Harriet Tubman was born just outside the hamlet; in her youth, she lived in her father's cabin nearb…Madison is an unincorporated community and census-designated place in Dorchester County, Maryland, United States. The population was 204 at the 2010 census. In the early 19th century, the community was a hamlet known as "Tobacco Stick." Around 1822, Harriet Tubman was born just outside the hamlet; in her youth, she lived in her father's cabin nearby, in what is now the Blackwater National Wildlife Refuge.