Lucky Knott, public information officer for the Coffee County Sheriff's Department, said he was not aware of Bell being on supervised release at the time the charges were brought against him.
Jerry Brinkley was with his two grandchildren when they saw the suspect, Michael Bell, flee the courthouse.
The prosecutor said Bassett went to a holding cell after Bell appeared in court.
"We have had an officer-involved shooting at our courthouse", said Coffee County District Attorney General Craig Northcott.
The Tennessee Bureau of Investigation said on Twitter that two Coffee County deputies were injured in the shooting Monday afternoon and are undergoing medical treatment.
One officer was shot and a second officer was shot and bitten by an inmate during a struggle over a weapon at the Coffee County Courthouse. He said both were in stable condition. Deputy Bowen underwent surgery.
Deputy Wade Bassett was transported to Vanderbilt University Medical Center in Nashville and deputy Wendell Bowen was transported from the scene to Erlanger Medical Center in Chattanooga for medical attention. Bell attacked Bassett and took his firearm after a struggle, Northcott said.
Bell then fled on foot, and, as Northcutt described, "as he was exiting the building, in a very unnecessary and cowardly way, he shot another deputy on his way out".
The Tennessee Bureau of Identification is investigating, and have confirmed that the inmate has died.
Northcott said that because of the ongoing investigation, the justice center court will be closed Tuesday, June 20. He entered the yard in another home before stopping and shooting himself in the head, Northcott said. Knott said the suspect may have been injured with a self-inflicted gunshot wound.