Fulton says a deputy shot 32-year-old Nathan Pierce when he tried to escape near a truck stop off Highway 82 east of Henrietta.
He says Pierce and the deputy got into an altercation, and they deputy's taser was knocked loose.
Fulton says Pierce grabbed the taser and charged the deputy with it, and that's when the deputy took out his gun and shot the inmate.
He says Pierce was then transported to United Regional where he later died during surgery.
The Texas Rangers are continuing their investigation into this incident.
Clay County Sheriff Kenny Lemons says the inmate was being transported in a van by Grayson County, and after the van pulled into the rest stop, the inmate was shot.
Sergeant Wheeler with the Grayson County Sheriff's Office says the deputy involved in the shooting is on administrative leave while the investigation continues.