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Council stakeholder engagement director Sian Sutton and environmental monitoring and operations director Scott MacLean left the council in November.
Council chief executive Sarah Gardner has continually declined to comment on either exit, saying they are personal matters.
On December 4, the Otago Daily Times requested all external and internal correspondence regarding these departures through the Local Government Official Information and Meetings Act.
The council extended the 20-working-day timeframe and responded this week declining the request.
Ms Gardner said she did not see the information as in the public interest.
The response implies the council contacted one of the former directors and attempted to contact the other.
''My decision to withhold this information for the grounds cited has been further strengthened as a result of this consultation.
''As you know, as a responsible employer we do not comment on individual staffing matters.''
When a third director, regional policy, planning and resource management director Tanya Winter, left in late December, Ms Gardner commented saying she did an ''excellent job'' leading the minimum flows project and building strong relationships with iwi and the community.