Jordan Boyle, of Dyhrberg Drayton Employment Law, was appointed to consider the complaints against Dunedin Mayor Jules Radich and city councillor Carmen Houlahan.
The complaint against the mayor came after an August radio interview in which he minimised the use of a racial slur by Strath Taieri Community Board chairman Barry Williams.
Cr Barker was deputy mayor when the complaint was filed against the mayor and she resigned from the role a few days later.
The investigations into potential breaches of the code of conduct follow confirmation Mr Williams breached the code by using a racial slur against a member of the public.
The Dunedin City Council decided in the public-excluded part of a meeting to censure Mr Williams and a letter to him from Mr Radich said the council was appalled by his behaviour, but the mayor then disclosed to RNZ the incident happened in a pub and he downplayed the significance of it.
Mr Williams and Mr Radich have apologised.
Just after the RNZ interview, Mr Radich told the Otago Daily Times he spoke to Mr Williams about the letter of censure and "suggested a path of contrition".
The ODT has requested, under the Local Government Official Information and Meetings Act, access to communication between Crs Houlahan and Barker, any written communication that may exist between Mr Williams and Mr Radich, and the independent investigator’s report into Mr Williams’ conduct.
All have been declined, so far, on the grounds information held by the council could form part of upcoming code of conduct investigations.
The city council also asked Mr Williams to consider resigning as board chairman.
He told a board meeting last month he had apologised in person to his victim, and he apologised to the public, but would not resign.
