The Mississippi State Insane Asylum opened in 1855 North of the city of Jackson. It was in operation at that location until March 1935, when it was moved to Rankin County and became Mississippi State Hospital (AKA "Whitfield"). The University of Mississippi Medical Center is now on the grounds of the old hospital with the address 2500 North State Street, Jackson, MS 39216.
There are some asylum records, sketchy at best at the Mississippi Department of Archives and History in Jackson. http://mdah.state.ms.us/
Asylum patients were enumerated in the federal censuses (1860-1930) by name. Patients who died after October 31, 1912 will have a death certificate often telling length of stay at asylum and the home town. Again check with the Department of Archives & History. A large number of patients were buried in the hospital cemetery (which for all practical purposes does not exist any more).