The dispute broke out as the National Health Service was preparing to hand a £110 million-plus contract for the provision of computer network services to a different company, ending the contract BT has with NHS Scotland.
BT said it has taken the "highly unusual" decision to start legal proceedings because it believes the tendering process was flawed "and did not make sure the contract was awarded on the basis of the most economically advantageous bid, in accordance with the relevant regulations".
The communications group is seeking a rerun of the bidding process, which took a year. Failing that, it wants £20m in damages.
NHS National Services Scotland (NSS) - which led the negotiations - has estimated the new deal would save the public purse around £300,000 a month. There is concern any major delay will prove expensive to the public purse, potentially jeopardising about £4m in savings over a 12-month period.
The new six-year contract is intended to bring the NHS, councils and ultimately other public-sector organisations onto the same information sharing network, Scottish Wide Area Network (Swan).
This, it is expected, will make it easier for information to be shared securely and cut costs arising from the numerous contracts with different firms. The move comes at a time when the Scottish Government is integrating the NHS and council-run social care services.
The Scottish NHS and six councils are involved in the first phase of Swan, but it is hoped this will expand significantly.
The contract is due to start in April - although NSS suggests the legal delay is already creating a work backlog.
A spokesman for NSS said: "By creating an IT platform that is open to all the Scottish public sector, the Scottish Wide Area Network will create savings that can be reinvested in essential public services.
"It will create common standards and easier integration between public sector bodies. The contract is worth approximately £110m initially, with the potential to rise as more public bodies make use of it."
Three companies were involved in the final selection stage of the bidding process: Cable & Wireless together with Virgin Media Business, a joint Capita-Updata Infrastructure team and BT.
A preferred bidder had been selected but not formerly announced when on December 6 BT served a summons on NSS initiating proceedings in the Court of Session.
A BT spokesman said: "We were naturally disappointed by this [contract] decision, particularly since the existing N3 national communications network operating across the NHS in Scotland has delivered significant benefits over many years. We believe our proposal offered excellent value and minimal risk to Scottish taxpayers.
"We can confirm that proceedings have commenced with a view to the procurement being rerun and hope this matter will be resolved shortly. This is a highly unusual step but we believe we have strong grounds for this challenge, which we believe is in the public interest."
NSS is going to the Court of Session in Edinburgh tomorrow in a bid to halt BT's legal action. A spokesman for NSS said it "managed a fair, robust and thorough procurement process".
He added: "Until this legal action is lifted or resolved, NSS cannot award the contract to the preferred bidder. NSS has commenced the legal proceedings required to lift the current action."
The BT spokesman added: "The reason we are going to court is that we think the tender process was flawed … As a result, we will argue that the process should be rerun.
"BT equally shares the NSS concern on value to the public purse, hence our reluctant legal action."