NICOLA Sturgeon’s husband should be investigated by prosecutors for giving false evidence under oath to the parliament, the Scottish Tories and Labour have said.

The parties said the Crown Office must probe SNP chief executive Peter Murrell after a “dismal and shifty” second appearance before MSPs this morning.

Mr Murrell repeatedly refused to give a straight Yes or No answer when asked if a statement he previously made to the inquiry under oath was false. 

He “absolutely refuted” the suggestion he perjured himself in December by giving contradictory accounts of a key meeting between his wife and Mr Salmond.

However he conspicuously refused to say if one of those accounts - that he was not at the couple’s home while the meeting took place - was a “false statement”.

Wilfully making a false statement under oath is punishable by up to five years in jail.

Mr Murrell was recalled to give evidence under a threat of compulsion after twice ducking possible dates after taking legal advice. 

In his evidence last year, he told the inquiry he was both aware and unaware that Mr Salmond would be visiting Ms Sturgeon at home on 2 April 2018.

He also said he was not at home while the meeting took place, then said he had been at home as the meeting was ending, having returned from work.

READ MORE: Nicola Sturgeon's husband Peter Murrell accused of giving unbelievable evidence to Alex Salmond inquiry

The meeting is crucial to the saga and possibly Ms Sturgeon’s future, as she has told Holyrood it was when she learned first Mr Salmond was under investigation by her officials for alleged sexual misconduct.

She also told parliament she took the meeting in her capacity as SNP leader, fearing he was about to resign from the party, so no government records were made.

Mr Salmond claims his successor is being dishonest and that she knew full well he wanted to discuss the Government probe, and that she even helped arrange the meeting four days earlier in her Holyrood office with Mr Salmond’s former chief on staff on that basis.

If Mr Salmond’s version is correct, it would mean Ms Sturgeon misled parliament and broke the Scottish ministerial code - a resignation offence which she denies.

At today’s evidence session, Mr Murrell repeatedly refused to give a Yes or No answer when asked if he made a false statement under oath when he said he was not at home that day.

READ MORE: Alex Salmond threatens to snub Holyrood inquiry over censored evidence

Tory MSP Murdo Fraser, who pressed Mr Murrell on the point, said afterwards: “Mr Murrell has given false evidence to parliament under oath.

“He gives the impression that he can say whatever he wants with impunity but in Scotland such actions must surely have consequences. 

“I intend to write to the Crown Office to ask them to investigate the matter.

“We had to drag him back to give evidence because of his previous contradictions around key aspects of his and his wife's actions in relation to the former First Minister.

“Today’s evidence session was no better. Mr Murrell seems incapable of giving a straight answer. His dismal and shifty performance was a masterclass in evasion.

“What was particularly craven was the attempt to use the female complainers as human shields to deflect the committee from getting the answers the public deserves.”

The inquiry is looking at how the Scottish Government botched its probe into sexual misconduct claims made against Mr Salmond by civil servants in 2018.

He had the exercise overturned in a judicial review, showing it has been “tainted by apparent bias”, a Government flaw that left taxpayers with a £512,000 for his costs.

He was later charged with sexuual assault but cleared on all counts at a High Court trial last March.

READ MORE: Alex Salmond inquiry: Nicola Sturgeon's husband Peter Murrell 'refutes' perjury claim but ducks key question

Last month, Scottish Labour also urged the Crown Office to investigate whether Mr Murrell had “perjured himself” in his December evidence, with a focus on his denials that text and WhatsApp about Mr Salmond involving him existed.

Pressed today by Labour MSP Jackie Ballie about his previous denials, Mr Murrell said he and SNP staff were clear that no messages within the inquiry’s remit existed.

Ms Baillie accused Mr Murrell of being “obstructive”, and reminded him he had been asked in December about any sort of messages, and he had not caveated his denials then.

She accused him of “dancing on the head of a pin” over definitions as he admitted there were other messages.

She said afterwards: “It is extraordinary that Mr Murrell may have exposed the false statements he previously gave to the Committee by admitting the existence of other messages under questioning today.

“The contempt that Mr Murrell holds for the Committee and its work is palpable, but that will not deter the Committee from holding him to account for his actions.

“I trust that the Crown Office will fully investigate the possibility that Mr Murrell has made false statements to the Committee.

“Misleading a Committee of the Scottish Parliament is tantamount to attempting to mislead the people of Scotland: for that Mr Murrell must be held to account.”

 Mr Salmond had been due to testify in person tomorrow, but pulled out in a row over the inquiry refusing to publish a submission in which he accuses Ms Sturgeon of misleading parliament.

He said he was willing to appear before MSPs up to February 16, when Ms Sturgeon is due to present her side of the affair, but on the strict condition the material is published.

His lawyers said that if it was not published under the inquiry’s authority, it could not be included in its final report.

Although already in the public domain, parliament officials and lawyers refused to let the inquiry publish it in case it breached court orders, data or privacy laws.

Asked for a response to the Crown Office demand, the SNP tried to pick a fight about Mr Fraser and Twitter.

An SNP spokesperson said: "Peter agreed - for a second time despite some committee members having prejudged his evidence already - to appear at committee and he answered questions honestly while maintaining anonymity of the women. 

"It is nothing short of disgraceful that some members of the committee are so willing to side-line the experiences of the women to try and score pathetic political points.

"Murdo Fraser's trolling tweets which mock the women's efforts to support one another are a disgrace. He should apologise and delete them."