Chancellor Frank Brown refused to grant a temporary delay of a runoff election slated for April 9.
Instead, a hearing will be held April 9 to decide if Councilman Peter Murphy has enough evidence to warrant a runoff, said City Attorney Mike McMahan.
The District 9 runoff has been in contention since the March 5 city election. Yusuf Hakeem won the election by six votes, and there were disputes about whether he had enough votes to get a 50 percent plus one majority as required by city law.
Murphy sued the Hamilton County Election Commission last week, saying it approved the election results with write-in votes counted, which would mean Hakeem did not have a clear majority.
The election commission disputes the accusations, saying computer software does not allow them to change votes.
Charlotte Mullis-Morgan, administrator of elections, said her office is prepared to hold a special election if needed.