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The council is obliged under the Audit Commission Act to disclose accounts information from the last financial year including contracts, invoices, receipts, and other information to local electors or anyone paying business rates in the area.
But IBM is attempting to prevent the council disclosing full information about its £400m contract, following requests for details about the deal by journalists at broadcaster ITV West.
The contract, the first of its type, brings together two public authorities and a police force into a "strategic partnership" organisation, which delivers IT, finance, HR, property procurement and customer contract centres.
IBM is the majority shareholder of the organisation, dubbed South West One, which was formed when Somerset County Council, Taunton Deane Borough Council and Avon and Somerset Constabulary signed the contract in September last year.
But the council said that "very late in the day" it received a request from IBM and SouthWest One for material from the contract to be treated as confidential.
IBM's approach to the council is likely to renew criticisms of excessive secrecy over the deal. The MP for Bridgwater, Conservative Ian Liddell- Grainger, told Parliament in March 2008: "SouthWest One is an outfit born in secrecy and reliant on secrecy."
There was an "unprecedented level of commercial confidentiality" during the procurement, according to a report by Dexter Whitfield, director and professor at the European Services Strategy Unit, for trade union Unison.
The council had planned to give a copy of the IBM contract to journalists at ITV West, based in Bristol, who have been investigating SouthWest One for several months. But the council withheld the information from them in line with IBM's request.
ITV West says it will go to court if its access to the documents continues to be denied.
Somerset said it was obtaining its own legal advice "as quickly as possible" on whether to release the information. A council spokesman told Computer Weekly that if it wrongfully discloses the information it may face legal action from IBM.
But any such action by IBM would be highly unusual - because the supplier is a partner of Somerset County Council in the SouthWest One joint venture.
ITV West had sought the disclosure of the contracts under the Audit Commission Act which is more powerful than the Freedom of Information Act. It requires councils to let local electors see contracts, invoices, receipts, books and bills that relate to the accounts of the recent financial year.
The withheld information includes payment arrangements, the service credit mechanism, the financial model, and the Joint Venture Agreement between IBM and the three public authorities.
An IBM spokesman said: "It is IBM policy not to comment on client specifics."
Critics of the deal including some local councillors are concerned the deal will fail and they want genuinely independent advice on whether it's too risky.
Somerset officials hope the contract will save about £200m - about half the total cost. They also hope the savings will fund a SAP-based CRM project which is due to be rolled out across the police and the two local councils.
ITV West's "West Eye View" is due broadcast a half-hour documentary, "Public Money Private Gain", on the IBM deal on Thursday at 7.30pm.