A Suspect In A Greeneville Shooting Took His Own Life In The Parking Lot Of The George Jaynes Justice Center In Jonesborough. It Happened Yesterday Afternoon Following A Chase With Police. Greene County Authorities Discovered A Female Shot At A Business On North Main Street. The Woman Later Died From Her Injuries. Authorities Located The Suspect And A Chase Ensued That Ended In The Parking Lot In Jonesborough. The Man Reportedly Got Out Of The Vehicle And Shot Himself. No Names Are Being Released At This Time. The Tennessee Bureau Of Investigation Has Taken Over The Investigation.