It is thought the complaint relates to opinion columns penned by Mr Hookway in The Northland Age.
In the first column, published on August 8, Mr Hookway described his difficulties getting timely and complete information from council staff.
In his next column, on August 22, Mr Hookway raised concerns about an unnamed council staff member he said was signing people up to a Facebook page supporting a new dog bylaw. That "did little to instil confidence in an unbiased policy development process", he said.
The day after the meeting Mr Hookway went on holiday to Tonga, and a supporter wrote a post on the Facebook page Kerikeri Notice Board stating that Mr Hookway had been "hauled over the coals by the 'pack'".
That sparked a social media storm, eventually prompting the council's communications team to contact the page administrators and warn them some comments were potentially defamatory.
In a follow-up post communications manager Richard Edmondson said such comments - specifically one labelling certain people as "wannabe Hitlers" - put not just the person writing the comments at risk of legal action but also the page administrators.
Administrators removed a post relating to the Kerikeri sewerage scheme while they sought legal advice.
Defamation can be defined as any untrue statement likely to harm a person's reputation. It is the equivalent in New Zealand law of slander or libel.
The council's code of conduct, adopted in December 2016, includes a rule that elected members must raise any concerns about employees with the chief executive; and that they should "treat all employees with courtesy and respect and avoid publicly criticising any employee".
Punishments for a "material breach" of the code of conduct range from a letter of censure to removal of privileges or, at the extreme end, "an invitation for the member to consider resigning".
Councillors cannot, however, be fired because they are elected by the public.
Complaints made under the code of conduct have to be made in writing to the chief executive. The chief executive then has to forward the complaint to an independent investigator for a preliminary assessment to determine whether it is serious enough to warrant a full investigation.
Mr Hookway has spoken out on a number of issues in his year so far as a councillor. He was instrumental in a council U-turn on demolition of the Kerikeri Domain pavilion.