A parallel investigation has found city councillor Carmen Houlahan has also brought herself into disrepute over multiple "unacceptable" texts to fellow councillor Sophie Barker.
An investigator found they both breached the code of conduct and the Dunedin City Council accepted the findings.
Cr Houlahan was asked to write a letter of apology and Mr Radich had already publicly apologised for comments he had made.
The breaches of the code were both considered to be material.
The complaint about Mr Radich arose after an interview by Radio New Zealand relating to the censure of Strath Taieri Community Board chairman Barry Williams for making a racist remark.
Investigator Jordan Boyle, a partner in Dyhrberg Drayton Employment Law, said Mr Radich's comments on the radio minimised Mr Williams' actions.
They also "ultimately led to the identification of the person who was subject to the comments from Mr Williams".
"It is important for people who engage in processes like this to have confidence their information will be kept confidential, particularly when they could face negative consequences if this confidence is breached."
Failure to keep the information confidential could bring both the mayor and council into disrepute, Mr Boyle said.
Mr Boyle said he considered the behaviour brought both the mayor and the council into disrepute.
The complaint against the mayor had been laid by deputy mayor at the time Sophie Barker and Cr Jim O'Malley.
This led to a series of text messages from Cr Houlahan to Cr Barker.
"Cr Barker found the texts to be aggressive, with their content having a devastating impact on her," a report for the council said.
She did not accept a September 11 apology from Cr Houlahan, as "it did not address the content of the texts, just the number".
Cr Houlahan said she accepted the findings.
"I have apologised to Cr Barker.
"I wish to move on from this and look forward to working positively with all my council colleagues in the new year."
Cr Barker said she was satisfied with the outcomes of both investigations, "which speak for themselves".
"I believe wholeheartedly that it's vitally important to be seen to uphold our code of conduct," she said.
"I made a principled decision to follow my beliefs and values, including integrity, and this often has difficult consequences, including my resignation as deputy mayor.
"Obviously, this process took a personal toll and has been a challenging couple of months to get through, so I'm relieved it's cleared up before Christmas."
