They've had a large Civil Defense siren system since the late 50s, which I'm sure they probably would have also sounded them for tornado warnings and other local emergencies. They had a huge system of dual tone Thunderbolts that covered mainly the most populated areas of Hinds County, and they later added some Federal RSH-10s (Thunderbeams) to the system in areas previously without siren coverage. The county unfortunately replaced the system about a couple of years ago, with new solar-powered Federal Modulator sirens, and I believe they may have already started removing the old system. Also from what I've been hearing, they've been having more problems with this new system in the past two years than they ever had with their old system over its long lifespan.
Here's a video someone took of the attack portion of one of their siren tests in Jackson, which features one of their old Thunderbolt 1000Ts, located next to fire station #17 at Wayneland Drive & Canton Mart Road.
http://www.youtube.com/watch?v=i_mlrdLr-9k
Google Street View of the siren:
http://g.co/maps/wzwz