Rollins said 24-year-old Brandon Jolvon Bethea of Fayetteville had been in court Tuesday and got into an altercation with detention officers when he was returned to jail.
Officers used a Taser - which emits a powerful electric charge - to control Bethea. They said immediately afterwards they noticed he was non-responsive and they began CPR until EMS paramedics arrived.
Bethea was taken to Betsy Johnson Regional Hospital in Dunn where he was pronounced dead at 2:14 p.m.
"Our thoughts and prayers are with the Bethea family during this difficult time," said Rollins in a statement.
Rollins said Detention Officer J. Clark - the officer who used the Taser - is on routine administrative leave while the SBI investigates.
Bethea had been in the Harnett County Detention Center under a $150,000 bond since January 23 after his arrest on two counts of attempted first-degree sex offense, attempted armed robbery with a dangerous weapon, possession of a firearm by a felon, and selling a counterfeit controlled substance.