The party demanded that one be held after SNP leader Nicola Sturgeon survived a vote of no-confidence in her leadership on Monday. It came after an independent adviser found that she did not break the ministerial code over her government’s botched handling of harassment complaints against Mr Salmond.
The former SNP leader was also acquitted of all criminal charges and successfully sued the government over its handling of the affair.
But Ms Sturgeon has not escaped entirely unscathed after a Holyrood committee inquiry concluded that there were “serious flaws” in the government’s approach.
A majority of its members also found that Ms Sturgeon had misled the inquiry in her evidence.
This triggered a vote of no confidence in the SNP-dominated Scottish Parliament – which Ms Sturgeon’s comfortably survived.
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Mr Fraser told the Scotsman that senior government officials should “consider their position” and that it was “time for someone to accept responsibility”.
In an interview with the publication, he added: “It seems clear that Nicola Sturgeon will refuse to abide by the principle of democratic accountability for her government’s monumental mistakes.
“The committee report indicates that even if the First Minister won’t be held accountable, numerous senior government officials should consider their position.
“It is time for someone to accept responsibility for letting women down, wasting more than £500,000 of taxpayers’ money, and the abundance of false and misleading statements from senior government figures.
“At every turn, the committee was obstructed by the SNP’s attempts to shut down scrutiny and keep key evidence secret.
“We have managed to produce a strong report that uncovers a great deal of what went wrong. But to uncover all the details, a judge-led inquiry is now necessary.”
On Monday James Hamilton QC, the Scottish government’s independent adviser on the ministerial code, found that Ms Sturgeon has not breached its guidelines over the Salmond affair.
Reacting to its findings, she said: “As I have previously made clear, I did not consider that I had broken the code, but these findings are official, definitive and independent adjudication of that.
“Today I want, once again, to remind people that at the heart of this case were women who had the courage to come forward and complain.
“That they were let down by the Scottish government’s handling of their complaints is not in dispute, and I again apologise to them for that.”
Its findings were also widely welcomed by SNP lackeys, but provoked outrage from some opposition parties.
Reacting to the news, Scottish Conservative leader Douglas Ross suggested the First Minister was still “not free and clear”.
He added: “The First Minister has been given a pass because it has been judged her ‘failure of recollection’ was ‘not deliberate’.
“I respect Mr Hamilton and his judgment but we cannot agree with that assessment. Nicola Sturgeon did not suddenly turn forgetful.”