"The threat of being told I'd breached the code of conduct has at times stopped me as a councillor from sharing important non-confidential information with the public.
"It is probably one reason many councillors won't speak to the media."
She said there should be rules around criticising council staff personally, but councillors needed to be able to query and offer constructive criticism about processes.
The code of conduct says councillors have a right to know of any investigation against them.
She said she felt what Jack had done amounted to an investigation against her.
A council spokesperson said it was a review and "no investigation was initiated".
"Councillors are always made aware in the event that a formal investigation is taking place."
Jack is on annual leave and was unavailable for comment.
Councillors agree to the "self-imposed" code of conduct when first elected, the spokesperson said.
"Given that these are adopted, they must not consider that these could possibly hinder their ability to undertake their duties.
"The code of conduct is a standard Local Government New Zealand with any minor adjustments agreed by council, and adopted (that is, agreed to) at the start of each three-year term."
Councillor Richard McGrath said the rules around councillors not saying anything negative against the council is a problem for democracy in the city.
"The best way to get good debate, and robust debate, is by being able to have both sides of the discussion or argument out there so you can work the pros and cons."
Councillor Kirsten Wise, who is running for mayor, said it was unacceptable for the CEO to use his position in this way.
Victoria University law professor Dean Knight told RNZ it was troubling if the code of conduct was being used "as a weapon" against elected members who disagreed with staff.
"If code of conducts are used to suppress half the conversation, the squeaky wheel, the uncomfortable naysayer, then we have an impoverished form of democracy."
