Police were called to the branch on Austhorpe Road in Crossgates at 2.50pm on Saturday, November 23.
A man had passed a note to staff demanding cash, but the panic alarm was activated and he left empty handed a short time later.
He was then chased away by a member of the public who lost sight of him down Back Aushtorpe Road.
On Monday, officers arrested a 21-year-old man in connection to the incident following a CCTV appeal.
He was later released under investigation pending further enquiries.