Cllr Simon Coles
Cllr Smith-Roberts was declared the winner by use of a computer algorithm - the modern equivalent of tossing a coin.
Cllr Coles had led the LibDems to power in the SWT local election in May 2019 and was seeking to take back the reins of the party.
But, as in a group vote after that election win, the vote was again tied.
Cllr Coles, who is also a county councillor, said the LibDem group holds an internal AGM every year just like any other organisation.
After the result was declared, he said: "I have said I will continue to support Federica of course.