Prosecutors are examining evidence given by witnesses in the Tommy Sheridan defamation trial against the News of the World.
Tommy Sheridan with wife Gail after his court victory
In a statement, the Crown Office said Crown Counsel had instructed the procurator fiscal in Edinburgh to examine the evidence of all witnesses.
A spokeswoman said this was "with a view to determining whether there is a basis for a criminal investigation".
Mr Sheridan, who represented himself, won his case and was awarded £200,000.
The process of examining evidence is expected to take several weeks.
The News of The World had claimed the former Scottish Socialist Party leader cheated on his wife and took part in orgies.
The tabloid appealed against the verdict, which its Scottish editor Bob Bird labelled "perverse".
He said it suggested 18 witnesses had committed "monstrous" perjury.
Conflicting evidence was heard concerning an emergency party meeting in November 2004 after the first sex claims about a "married MSP" were published by the tabloid.
Eleven party figures, including current party leader Colin Fox and MSPs Rosie Kane and Carolyn Leckie, told the trial that at that private meeting Mr Sheridan had admitted visiting a swingers club in Manchester.
Their claims were supported by minutes of the meeting which were produced in court, but described as "dodgy" by Mr Sheridan.
Four of Mr Sheridan's party colleagues, including MSP Rosemary Byrne, backed his account of the disputed party meeting, claiming that he had never made any such confession.
The 23-day trial also heard claims from three witnesses that they had sex with Mr Sheridan.
On Tuesday, the Socialist MSP said: "The Crown Office is duty-bound to respond to complaints from members of the public.
"I believe they have received complaints from Brian Monteith - a right-wing independent MSP - and a member of the SSP executive committee.
"With such an unholy alliance seeking action, the Crown Office probably feel obliged to respond."
Mr Sheridan's parliamentary ally Ms Byrne said: "The decision by the Crown to investigate witness statements in a recent court case does not surprise or interest me.
"I understand that they have had a complaint and that they must follow complaints up."
A News of the World spokeswoman said she welcomed the "investigation".
A spokesman for the Scottish Socialist Party said: "The procurator fiscal has been given a job to do.
"We simply reaffirm that the 11 witnesses from the SSP have nothing to fear from any inquiry."
The solicitor for two key witnesses who gave evidence against Mr Sheridan also welcomed the Crown Office investigation.
Anne Colvin, 54, and Helen Allison, 52, told the trial they had seen the MSP in a three-in-a-bed orgy at a Glasgow hotel in June 2002.
Solicitor Martha Rafferty, of Anthony Mahon and Co, said: "I've spoken to my clients and they are delighted with the announcement from the Crown Office.
"My clients have always maintained they told the truth under oath."