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The complaint against Cr Hudson was detailed in a letter by Chisholm Park Golf Club golf professional Andrew Whiley to Mr Chin on Friday.
Mr Chin yesterday confirmed the complaint had been received, and said he would "deal with it under the formal process available to me".
He declined further comment.
Mr Whiley confirmed he had laid the complaint after receiving a phone call from Cr Hudson immediately following a death at Lawyers Head on Thursday.
Mr Whiley had spoken to media earlier in the week, expressing concern at the location of a planned security fence.
Cr Hudson could not be reached for comment yesterday.
Under the council's standing orders, a code of conduct committee could investigate complaints.