Cr North had previously supported the referendum and confirmed before the last council elections in 2017 that his position had not changed. He voted as recently as last month to back the referendum.

But on Wednesday night he was the only councillor to change the way they had voted on the issue at the June meeting of Bathurst Regional Council with Cr Jacqui Rudge, who was absent in June, voting in support of a referendum.

Cr North acknowledged Cr Bourke would be angry with his decision but said he had become increasingly concerned that a popularly-elected mayor could not be moved on by councillors if they were not performing.

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"I've spoken to a councillor on another council ... and they're at the stage with their popularly-elected mayor that [even though] it's going to do nothing, they're potentially going to make the statement of a no-confidence motion because the person has lost the floor," he said.

"This councillor has spoken to a number of other councillors with a popularly-elected mayor and found the same sort of thing."

Cr North said a lot of people in the community could not make an informed decision on who should be mayor. "They don't really care about local politics," he said.

A clearly frustrated Cr Bourke said he was not surprised by Cr North's backflip.

"I was voted in - probably the most popular councillor elected at the time - and I didn't go for the mayor's job, did I? No," he said.

"I went in there to support the mayor as I've supported all the other mayors we've had to work with.

"Other councillors here haven't always supported the mayor and there's always backbiting and fighting within the chamber.

"So let's hear what the community has to say by having a referendum and asking them. That's all I'm saying."

Earlier, general manager David Sherley responded to a question from Cr Jess Jennings by saying that he could not recall a referendum on a popularly-elected mayor ever being defeated.

"So," Cr Jennings told his colleagues, "that says to me ... we're not actually voting on whether or not people get a say [but] whether or not we are going to have a popularly-elected mayor.

"If you're against a popularly-elected mayor, you should be voting no tonight."