Dunedin City Council says an Act of Parliament stops it reducing the salary of the chief executive of the Otago Museum.
Scrutiny of the museum's activities is increasing after disclosures in January that Shimrath Paul received a package worth $310,793 in 2011, higher than that of the head of Te Papa, the national museum.
Earlier this week, a Dunedin council committee received a report showing that under the Otago Museum Trust Board Act, the museum is fully independent.
It says the most councillors can do is to request more information on matters of interest, submit to museum annual plans and ask the board's chairperson to attend meetings.
The Dunedin Ratepayers and Householders Association says the council must cut the museum's funding to force a salary reduction.