Alex Hollingsworth, the leader of Oxford City Council, has been challenged to make public a report into how much value for money the Town Hall is providing.
The council has appealed against a judgment by district auditor Andy Burns in his full-term report on the authority, specifically on how it makes use of its resources and provides value for money.
Many local authorities across the country published their inspection reports by the March 31 deadline but, because of Oxford's appeal, the auditor's judgement will now not be known until after the city council elections on Thursday, May 4.
Opposition councillors have claimed this is a political stunt and have challenged Mr Hollingsworth to publish it early.
However, Mr Hollingsworth said "it would be silly" to do so before the district auditor had finished studying it.
In an open letter to Mr Hollingsworth, John Goddard, leader of the city council's Liberal Democrat group, said: "Are you afraid the Audit Commission's judgment is as damning as their verdict two years ago that the council is weak' the only weak council in the county?
"The device of delaying by making an appeal is not to try to alter a favourable assessment. So the only question is just how unfavourable is the commission's assessment.
"I challenge you, Alex, to publish, now."
The Audit Commission's annual report on the state of the council is a public document and forms part of the public spending watchdog's national inspection of councils.
Asked if he would make the report public, Mr Hollingsworth said: "Not until the district auditor has finished studying the challenge. That would be silly.
"The vast majority of the report is very good, but I am not going to publish something that is being challenged."
Mr Burns's report will also contain details about whether the council received the best price for land it sold to Firoz Kassam, the former chairman of Oxford United, in 2001.
Mr Kassam's consortium Firoka Ltd purchased the land in Blackbird Leys on which the Kassam Stadium is now built for £1.3m, but the implication is this was not its true valuation.
Oxford Green group leader Craig Simmons said: "Most local authorities have published their reports, even if they have then gone on to challenge them, rather than bury bad news.
"If they have nothing to hide, why aren't they publishing the report?"
Stuart Craft, leader of the Independent Working Class Association, added: "We are all for openness and we stand for transparency Labour is on a hiding to nothing at the elections and is doing everything it can to save face."
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