Chisholm Park Golf Club golf professional Andrew Whiley laid the complaint against Cr Hudson on September 25.
He wrote to Mayor Peter Chin the day after he claimed Cr Hudson, during an angry exchange over the telephone, linked him to the death of a man at Lawyers Head on September 24.
Contacted yesterday, Mr Whiley said he had since met Mr Chin and reiterated he wanted the complaint investigated, but was still waiting for an outcome.
An email sent to Mr Chin on Monday, requesting an update, had not been answered.
Mr Chin said yesterday he was still working on the complaint and declined to say when he expected the matter would be resolved.
"I have said I would deal with it and I will."
Mr Whiley's exchange with Cr Hudson came after Mr Whiley questioned plans for a new security fence at Lawyers Head.
Mr Whiley said he had received a letter from Cr Hudson, following his meeting with Mr Chin, offering a one-line apology "if I have offended you".
Cr Hudson defended his actions when contacted yesterday, saying he had spoken to Mr Whiley as a private citizen - not a city councillor.
He said he had phoned Mr Whiley only to pass on information relayed to him by members of the public and took issue with Mr Whiley's version of their conversation.
He conceded he was "pretty upset" and the conversation had become heated, but did not feel an apology was necessary and had written one only at Mr Chin's request.
"If I offended him I was quite happy to apologise . . . but no, I don't feel an apology was necessary," Cr Hudson said.
He expected to meet Mr Chin again next week, and said it was "not true" the complaint was not being investigated.
