A Traffic Penalty Tribunal spokesman said the council had submitted an application for a review of adjudicator Stephen Knapp's decision last month, which left the council at risk of having to refund 48,000 motorists' fines.
He said a second adjudicator from the tribunal was now conducting that review, but he could not say when his or her decision would be announced.
He said that if the reviewing adjudicator upheld Mr Knapp's decision, the council would have to accept the ruling unless it decided to apply to the High Court for a judicial review - as it was entitled to do. He was unable to disclose details of the council's arguments in its application.
Mr Knapp said in February that neither of the schemes banning cars from Coppergate and Lendal Bridge could be "sensibly" described as bus lanes, meaning the authority had no power to issue a penalty charge notice.
He said there was an "inherent ambiguity" in the signs advising drivers of the Lendal Bridge restrictions, because the direction sign did not include the times of the closure.
He also found that the signing at either end of Coppergate was not adequate to reasonably alert the driver to the terms of the restriction and the signs were poorly located.
Top traffic lawyer Nick Freeman, known as 'Mr Loophole' for his success in defending celebrity clients, said the council should reimburse all penalty charges paid by motorists.
But city leaders later said that after receiving independent legal advice from a leading legal expert in the field, the council was confident both schemes were operating within the law.
However, officials warned councillors earlier this month not to spend any of the £700,000 it earned from the Lendal Bridge closure until the legal wrangle over the trial was over and the authority was certain it would not need to refund all the fine cash. The bridge has been re-opened.
Darren Richardson, director of City and Environmental Services, said: “City of York Council has written to the Traffic Penalty Tribunal to notify them that the authority is challenging their decision on Lendal Bridge and is now awaiting the outcome of that review.”