Probe over property deals on behalf of Michelle Thomson MP
Police Scotland is investigating alleged irregularities with property deals carried out on behalf of the SNP MP Michelle Thomson.
The transactions, in 2010 and 2011, led to a solicitor being struck off by the Law Society of Scotland.
It referred the case to the Crown Office, which has instructed the police investigation.
The Edinburgh West MP has denied any wrongdoing but has withdrawn from the party whip.
The BBC understands the initial police inquiries will not involve Ms Thomson, who was the party's business spokeswoman at Westminster.
The investigation relates to solicitor Christopher Hales who was struck of last year for professional misconduct.
He did work for Ms Thomson and it has now emerged that all 13 of the transactions he was struck off for involved her or M&F Property Solutions, a firm in which she was said to be a partner.
After a hearing in May 2014, the Scottish Solicitors' Discipline Tribunal said Mr Hales failed to provide mortgage companies with key information used to prevent fraud and must have been aware that there was a possibility he was facilitating mortgage fraud, whether or not it occurred.
In some cases, loans obtained for the properties were greater than the actual purchase price.
Official documents from the hearing set out Ms Thomson's role in the mortgage deals.
The Law Society said it first raised the case "informally" with the Crown Office in December last year but then made a formal referral in July 2015.
In a statement released on Tuesday evening, Ms Thomson said she would "cooperate fully" with the police inquiry if she was required to do so.
She added: "I have always acted within the law and look forward to being cleared of any wrong doing.
"I have this afternoon decided to withdraw from the party whip whilst an investigation takes place.
"Once the investigation is concluded I look forward to returning to play a full role in party activities."
Her withdrawal from the whip means she is no longer a member of the parliamentary party and will not speak for the SNP on business issues at Westminster.
An SNP spokesperson added: "In line with party rules Michelle Thomson's decision to withdraw from the party whip means her party membership is also suspended."
Analysis by Glenn Campbell, BBC Scotland political correspondent
What a difference a minute makes.
At 18:22 the SNP issued a statement on behalf of Michelle Thomson MP.
It confirmed that she would not represent the party while the police investigate property transactions carried out on her behalf.
The statement reads:
"I am aware of the police investigation and will cooperate fully if required to do so. I have always acted within the law and look forward to being cleared of any wrong doing. I have this afternoon decided to withdraw from the party whip whilst an investigation takes place. Once the investigation is concluded I look forward to returning to play a full role in party activities. I will be making no further comment on this matter."
Yet just one minute earlier, at 18:21, a statement issued by Michelle Thomson's personal media adviser made no mention of her stepping down from SNP duties.
"I am aware of the police investigation and will cooperate fully if asked to do so. I have always acted within the law and look forward to being cleared of any suggestion of wrongdoing. I will be making no further comment on this matter."
Makes you wonder whether she really did jump or was she pushed?
Either way, she is no longer the SNP's business, innovation and skills spokesperson at Westminster.
Ms Thomson, a prominent figure in the pro-independence campaign group Business For Scotland ahead of last September's referendum, is reported to have built up a large "buy to let" property portfolio.
She was one of 56 SNP MPs elected to Westminster in the general election in May after winning the seat of Edinburgh West and was appointed the party's spokesperson for business, innovation and skills.
Opposition parties have now called for the SNP to reveal how much was known about her business dealings.
A Labour spokesperson said: "It is now vital that the SNP come clean about this situation, and who knew what, when.
"The first minister and senior SNP party officials have serious questions to answer. Did Nicola Sturgeon know about these allegations before Michelle Thomson was approved as a SNP candidate for the general election?
"When did senior SNP officials first become aware of the allegations and did they investigate them?
"Michelle Thomson was vetted by the SNP and deemed to be an acceptable candidate for an election. Senior cabinet ministers have backed her citing her business dealings. Now she is withdrawing from the party whip, and resigning from the SNP as an investigation takes place."
Scottish Conservative chief whip John Lamont said: "Having tried to ignore these serious allegations for 48 hours, the SNP has hit the panic button.
"The SNP needs to explain very clearly what they knew about Ms Thomson's business dealing and whether they were aware of her connection to these property deals when she was being selected.
"The SNP promised a new politics at Westminster. It has taken a matter of weeks for their shine to wear off."
Deputy First Minister John Swinney said: "It is important that any allegations that are put forward in this matter are fully and comprehensively answered by Michelle Thomson."
A Police Scotland spokesman said: "Police Scotland can confirm that as a result of a complaint from the Scottish Solicitors' Disciplinary Tribunal, it has been instructed by the Crown Office to carry out an initial investigation into alleged irregularities relating to property deals in the year 2010-2011."
Lorna Jack, chief executive of the Law Society of Scotland, said: "If the Law Society has concerns about any potential criminal matter arising from a SSDT finding, it will refer the matter to the appropriate authorities.
"In the case of Christopher Hales, we first raised this informally with the Crown Office in December 2014. Our Guarantee Fund sub-committee referred it formally to the Crown Office in July 2015."