The Conservatives took control of Somerset County Council this year.
A political row has broken out in Somerset over a joint venture company set up to manage many of the county council's management functions.
The firm, SouthWest One, is 75% owned by IBM, who will make £400m over 10 years from the contract.
County council leader Ken Maddock said he wants an inquiry into the deal, signed by his Lib Dem predecessor.
However Lib Dems on the authority have accused Tory Mr Maddock of being secretive about the planned probe.
At a meeting of the council, news emerged of the planned inquiry from a communication seen by the leader of Taunton Deane Borough Council.
The borough council is another partner in SouthWest One.
Liberal Democrats said they should have known about the probe and they were suspicious of the fact Mr Maddock had changed the council's rules to restrict the access to information enjoyed by council members.
Lib Dem Councillor Sam Crabb said the change went against the Conservatives' national policy, which called for openness.
"Inevitably we will have to put in requests under the Freedom of Information Act and that is going to be time-consuming and costly for the council," he said.
Mr Maddock told the BBC the council had had to change its information policy because of "three high-level leaks" of sensitive information in recent weeks.
Speaking about the SouthWest One contract inquiry, he said: "It's just a discussion at the moment.
"I think we are entitled to a bit of space while we work out what is the best way forward."
SouthWest One, which was set up in 2007, runs IT facilities and services such as finance and benefits for Somerset County Council.
It has attracted controversy over the way it was set up, with Conservatives and other critics claiming people were kept in the dark over the contract.
Bridgwater MP Ian Liddell-Grainger claimed in Parliament: "The architects of the joint venture company have strangled information to such a tiny trickle that nobody outside the magic inner circle knows what is going on."
Earlier this year, there was controversy when contractors supplying Somerset County Council said the SouthWest One's IT systems meant their invoices were not being paid.
SouthWest One says pooling services and drawing on IBM's expertise is saving Somerset tax-payers £20m a year.