The City of Lincoln Council poll last Thursday resulted in Conservatives and Labour having 16 seats each.
Despite the cordial relations developing in Westminster between Deputy Prime Minister, Nick Clegg amd Prime Minister David Cameron with thier coalition government, Cllr. Mrs. Heath has told the Lincolnshire Echo that no-one was dictating her decision.
A spokesman for the Liberal Democrats told the paper that the party believes in 'localism and the right of locally elected representatives to make decisions'.
Cllr. Mrs. Heath is understood to be in talks with both Conservative and Labour groups. Whichever side she backs will in theory have the majority of the votes.
If she backs nobody, the Conservatives may still lead the next council as the new mayor, who is a Conservative Councillor, will have a casting vote.
The current deputy mayor, Cllr. Geoff Kirby, Conservative (Hartsholme Ward) is set to be made mayor on Tuesday, 25th May 2010.
Cllr. Mrs. Heath told the Lincolnshire Echo:
"I am not looking for concessions and I won't be taking anyone's whip. I will essentially be taking an item by item approach. I am not prepared to make a decision at the moment."