Conran is an unincorporated community in eastern New Madrid County, Missouri, United States. In Law, an unincorporated area is a region of land that is not a part of any Municipality. New Madrid County (pronounced New MA-drid short a as in "mad" is a County located in the U Missouri ( or) is a state in the Midwestern region of the United States bordered by Iowa, Illinois, Kentucky, Tennessee The United States of America —commonly referred to as the It is located about ten miles southwest of New Madrid on U.S. Route 61. New Madrid (nuːˈmædrɪd is a city in New Madrid County, Missouri, 42 miles (68 km south by west of Cairo Illinois, on the Mississippi River US Route 61 is the official designation for a United States highway that runs from New Orleans Louisiana, to the city of Wyoming Minnesota.