"We will not confirm details of either complainants or the person or persons who were complained about. We cannot comment on individual employment matters," he said.
The Herald has sought comment from the woman.
Wilson said he believed the council is a safe place to work with the necessary resources and mechanisms in place for reporting and responding to allegations of bullying.
The bullying allegation comes after chief executive Jim Stabback launched an internal review into the council's policies, processes and procedures around stress and mental wellbeing following the tragic deaths of two staff in December.
The two deaths are unrelated to each other or the manager who left.
Jenny Gargiulo, a principal environment specialist, died on December 1 amid claims she had been bullied and harassed.
The coroner is looking into her death, which a spokesman said was suspected to be self-inflicted.
A few days later, a member of the council leisure team lost his life in a similarly tragic way.
Gargiulo, who was responsible for implementing the council's weed management plan that included the controversial use of the chemical weedkiller glyphosate, was believed to have come under a lot of pressure.
In a Facebook post, councillor Richard Hills said he knew Gargiulo put up with a lot from members of the public and elected members.
Wilson said council staff often come under pressure and intense criticism from the public.
"We have seen a steady increase in violence, harm and unacceptable behaviour directed towards our staff and elected representatives in recent years," he said.
In mid-December, councillors received a report based on two staff surveys showing they had been struggling with the pressure of the post-lockdown work environment, with concerns about their stress levels and wellbeing.
In late 2019, the Herald broke the story of aggressive behaviour by a senior council officer. In that case allegations, made by a council whistleblower and confirmed by multiple sources, included an incident at an All Blacks test against France at Eden Park, an expletive-ridden after-hours phone call and mediation with a colleague.
Sources described the officer as "bombastic" and having an "aggressive tone and behaviour".
The senior officer no longer works at the council.
Wilson said seven council staff lost their jobs for bullying between 2015 and 2019. A further 14 staff received written warnings and a further five received final written warnings, he said.