Thames-Coromandel mayor Sandra Goudie is providing no comment on whether or not she is yet vaccinated against Covid-19 - but she can attend meetings regardless after staff changed the council's vaccination policy.
Councillors say they are getting no answers from the mayor on her vaccination status, and at least one has vowed to walk out if she attends a meeting in person.
Another called changes announced on Monday to the council's policy allowing unvaccinated people to attend council meetings "disgraceful".
Goudie - after previously going public that she had not got vaccinated - is tightlipped on her vaccination status.
"No comment," she said.
Although the TCDC's initial policy on vaccination had input by full council, staff amended it to allow unvaccinated staff, elected members and contractors to attend meetings if they provide a negative Rapid Antigen Test (RAT).
Ratepayers will pick up the cost for council's unvaccinated staff to do rapid antigen tests for "critical" meetings - those deemed so by the TCDC chief executive or a group manager.
The cost will not be picked up by ratepayers for unvaccinated elected members or contractors.
Councillor Gary Gotlieb said the policy change was "disgraceful".
"There was no discussion that [the policy] would be changed and I don't understand why it would, particularly now that we've gone into red.
"A 72-hour test is so unreliable.
"I just feel they're thumbing their noses at us and the ratepayers. "
Chief executive Rob Williams said the policy was reviewed by senior management, HR staff, risk and H&S professionals.
"There was good discussion and no objections.
"The main consideration was to ensure that general managers have the opportunity to stay in close contact with all staff but for those unvaccinated staff that are forced to work from home, they will be able to attend critical management/team related/HR meetings face-to-face while we have no community transmission in the district."
He did not respond to questions from councillors that the policy had been implemented to allow Goudie to attend if she was not vaccinated.
Councillors spoken to by the HC Post say the first they learned of the policy amendments was reading a published statement and would not have supported it.
Southeastern ward councillor Terry Walker said there was no discussion with other elected members, unlike the initial policy on vaccination for those entering the council.
"The mayor had to be vaccinated by 17 January and she hasn't fronted to say she has done that. There's so much uncertainty about the whole thing," he said. "But in my view, if there's rules, there's rules."
Now that the policy has been amended, unvaccinated elected members, TCDC staff and contractors who give formal confirmation of a negative Covid test within 72 hours of the beginning of the meeting time can attend any meeting with approval by a group manager or the chief executive.
Cr Rob Williams, who has resigned and is due to finish in late February, said if Covid cases appeared in the community then this policy would again be reviewed.
"Our aim during a period where there is not yet any community transmission in our district is to keep all of our staff connected and monitored for their wellbeing and performance.
"If we do have confirmation of community transmission in our district, then we'll review our policy again."
The council defines vaccinated staff as someone who has had two doses of the Pfizer or Astra Zeneca Covid-19 vaccination. A third booster shot is not required as part of the policy.
Gotlieb is in Wellington and unable to attend a meeting on Tuesday - the first time elected members will meet since December - but he and Walker believed ratepayers would not be happy with the amendment.
Walker said if he knew Goudie was attending a meeting in person: "I would not turn up".