The possibility of a complaint being laid was raised after a meeting last week when Crs Gerry Eckhoff and Brian Scott raised questions about whether chairman Stephen Cairns was "compromised" because of his role as a commercial property valuer and developer.
Other councillors were not happy with the way the two councillors raised the issue.
Mr Martin said the process, which had never before been needed, had to run its course "as and when it happens".
While the public's right to know was important, some things were "strictly internal" and should stay out of the public domain, he said.
"It is inappropriate on anyone's part to forward speculate and that should not be taken as a presumption something is, or is not happening."
Deputy chairman Stephen Woodhead yesterday declined to comment further at this stage.