The incident began about 7:30 a.m. at the Kwik Shop Discount Tobacco and Grocery Store on U.S. Highway 301.
Witnesses said the victim's name is George McEachin. He lived in the Green Manor Rest Home, which is about a quarter mile from the store on Parkton Tobemory Road.
According to eyewitnesses, McEachin came into the store and started throwing drinks. They said he then went outside and had confrontations with a customer and a man who was refilling the gas tanks.
When officers caught up to McEachin, he was back at the rest home. That's when they used their Taser to get McEachin under control.
It is unclear if he died at the scene or at the hospital.
People who know McEachin said he was normally a nice guy, who sometimes pumped gas for customers at the station.
McEachin was allegedly on medication for mental problems.
It will be up to the medical examiner to determine the exact cause of death.
The SBI is investigating.