On February 1, 2010, at the bank's Fyshwick branch in Canberra, a balaclava-clad robber had threatened to shoot the customer Gary Roberts if the bank teller did not hand over money, the court heard.

But the teller activated the security screens.

The robber yelled "I f---ing warned you", fired the gun, and fled.

Mr Roberts developed chronic post-traumatic stress as a result.

He had argued before a judge earlier this year that Westpac owed him, as a customer, a duty to take reasonable care not to increase the risk of harm to him from an armed robbery.

The bank should have, he argued, properly trained its bank tellers and staff to always obey an offender's instructions during a robbery.

The arguments were rejected by Acting Justice Linda Ashley, who found the bank had no control over an armed robber's conduct and that it was not liable for Mr Roberts' post-traumatic stress.

And on Tuesday, Chief Justice Helen Murrell handed down a judgement of the ACT Court of Appeal, which included the reasons of Justices John Burns and John Gilmour, dismissing Mr Roberts' appeal.

Their Honours found the first judge had, correctly, found there was no duty owed, and if it were, it was not breached by the teller's act of activating the security screens.

Justices Burns and Gilmour said the question of Westpac's control over an offender coming onto its premises was the dominant one in establishing whether or not the duty existed.

While it was accepted by Mr Roberts that the bank had no control over the robber, the judges said Mr Roberts' case came down to the man's fundamental suggestion Westpac could exercise control over its employees, whose actions could impact the conduct of an offender.

But, "Westpac did not have any indirect practical control over the offender by its control over its staff ... as to how they must respond when confronted by an armed offender," the judges said.

"Inability to control the conduct of an armed offender in this indirect way is an unassailable obstacle to the imposition of such a duty."

Further, they said, the relationship of banker and customer does not create a special relationship giving rise to that duty of care, despite a "colourful" submission describing Westpac's banking activity as one that "lured" robbers to its premises.

On the question of the breach of the supposed duty, Justices Burns and Gilmour said the suggestion the bank should have trained staff to always obey a robber's instructions was both impractical and unreasonable.

"Indeed such an inflexible instruction to staff, who are themselves likely victims of harm in an attempted robbery, would likely be a breach of the bank's duty to staff, should compliance with that instruction be causative of their harm," they said.

The court ordered Mr Roberts pay Westpac's costs.