Commissioners Tim Hagan and Peter Lawson Jones claim a "performance audit" is needed to restore shaken confidence in Russo and his office's role setting values on property.
Russo's former assistant, Sandy Klimkowski, has told investigators that Russo accepted $1.2 million in bribes over an extended period from lawyers for V.A.S., a firm that Russo hired to appraise commercial property.
Commissioner Jimmy Dimora, also a target of the federal corruption probe, signed letters, along with his fellow commissioners, requesting state action.
But Dimora called the request "meritless and useless."
Federal investigators have most of Russo's records.
For the state to get involved, Russo must request the additional audit. And Russo spokesman Destin Ramsey says Russo will not make such a request.
He says that would be a waste of taxpayers' dollars because two audits that are done or in progress have not yet been released.
Attorney General Cordray is expected in Cleveland Friday to announce what action his office will take.