Investigators say Mahlon Hebron somehow obtained keys inside the jail and made his way to the roof before attempting to climb over two exterior security fences.
Officials said Hebron was unsuccessful and injured himself during the attempt. He landed in gravel between the two fences and never made it outside the facility's secure perimeter.
Hebron remains in custody at the jail. He is charged with killing his girlfriend, 37-year-old Tiffany Lassiter, in Henderson on Christmas Eve last year.
The attempted escape comes just weeks after two other inmates escaped from the same jail.
Investigators are now working to determine how Hebron was able to obtain access to the jail keys.