It comes just days after similar legislation was scuppered at Westminster.
Sturgeon Slams 'Ridiculous' Candidate Claims
It is "ridiculous'' to suggest the SNP would allow a candidate to be put forward for election knowing there were "serious problems'' over their integrity, the First Minister has said.
Nicola Sturgeon was challenged on the party's knowledge of MP Michelle Thomson's business dealings after it emerged she is to help police with their inquiries into property deals conducted five years ago.
Ms Thomson, who was elected as the member for Edinburgh West in May, has denied any wrongdoing and has withdrawn herself from the party whip at Westminster.
Ms Sturgeon has said the SNP did not know about MP's business dealings until reports began to emerge in the newspapers.
Speaking at First Minister's Questions, she said: "I said yesterday, I have said again today: the SNP had no prior knowledge of these issues.
"Of course, as I also have already said, Michelle Thomson denies any wrongdoing, therefore presumably she would maintain that there was nothing for her to have brought to the attention of the SNP.
"Our vetting procedures as a party are robust but we keep them under review, as I would hope every political party does.
"While we make all reasonable checks and ask all reasonable questions, by definition it is not reasonable to expect that matters of which we have no knowledge can be investigated.
"But what is also ridiculous to suggest of any political party is that any party would knowingly allow a candidate to go forward for selection knowing there were serious problems about the integrity of that individual candidate.
"If there are matters that are proven to have been done wrong, then these will be serious issues that the SNP will respond to.''
Ms Sturgeon said Ms Thomson was entitled to a presumption of innocence and warned against the temptation "in the hurly-burly of politics to seek to pre-judge issues''.
Labour's Kezia Dugdale accused the SNP leader of "running away'' from Ms Thomson, who was the SNP's Westminster spokeswoman for business, innovation and skills.
"This is a First Minister who claims that nobody in the SNP knew anything about that, and I will take her word for that,'' she said.
"But now she does know. She knows that an elected representative in her party acted in a way that is unacceptable.
"This is someone that the SNP did know.
"The First Minister has spent two days running away from Michelle Thomson as fast as she can, but isn't it the case that for the last two years Michelle Thomson has been right at the heart of everything the SNP stand for?''
Ms Thomson has been linked with property deals involving Christopher Hales, a solicitor who was struck off by the Scottish Solicitors' Disciplinary Tribunal (SSDT) in May last year in connection with 13 transactions in 2010 and 2011.
Prosecutors have instructed police to carry out an investigation into ''alleged irregularities'' relating to property deals in the year 2010/11 after the case was referred to the Crown Office by the Law Society of Scotland.
The society said concerns over potential criminal matters relating to the tribunal's findings were first raised ''informally'' with the Crown Office in December 2014, and then ''formally'' in July this year.
Ms Dugdale said: "I am not prejudging anything.
"The facts are undisputed: a tribunal issues a damning verdict, that is a fact. A lawyer was struck off, that is a fact.
"The Crown Office was made aware of concerns, that is a fact. Vulnerable families lost out.''
Ms Sturgeon said: "Kezia Dugdale is right when she says that it is a fact there has been a solicitors' disciplinary tribunal, she is also right to say it is a fact that a solicitor has been struck off.
"Neither of those things prove the guilt of anything of any other person.''
The First Minister added that a police investigation was under way and should be allowed to run its course.
The Labour leader responded: "I am not asking the First Minister to comment on the specifics of a live investigation because I accept that criminal matters are for the police.
"But this is also a moral matter, and I would expect her to comment on that.
"What we have here is vulnerable families losing out for the financial gain of others.
"Vulnerable people being taken advantage of, as their homes are snapped up at knockdown prices.
"Can I ask the First Minister, does she agree with me that profiteering from vulnerable families is just plain wrong?''
Ms Sturgeon said: "Kezia Dugdale, although she disagrees with me, as she is entitled to do on a whole range of issues, I hope would accept that my commitment to social justice, and helping vulnerable people, like her's, is beyond any question.''
Ms Sturgeon said if the allegations are proven to be correct they will "represent behaviour that I find completely unacceptable''.
Conservative leader Ruth Davidson cast doubt over Ms Sturgeon's insistence that she knew nothing about the allegations until she read them in the newspapers.
"We already know that the Crown Office and Police Scotland were asked whether they would investigate this case in July of last year,'' she said.
"We know that the Law Society raised with the Crown Office in December.
"We know that journalists have been investigating it all summer and we know that the police were called in nearly three months ago.
"Yet the First Minister is asking us to believe that nobody in the SNP, the party of government, from the constituency in Edinburgh West right up to the chief executive to the leader herself, knew anything about this until they read it in the paper almost two weeks ago.
"Does the First Minister think this sounds believable or is it the case that somebody somewhere turned a blind eye?''
Ms Sturgeon said: "I do think that reasonable people listening to the answers that I am giving will opt to believe that that is the case, because I would not stand here and say it was the case if it wasn't the case.
"Ruth Davidson says that 'we all knew' ... did she know any of that before the Sunday Times published these stories?
"Because I certainly didn't know these stories until they came to light in the media.
"The fact of the matter is we had no prior knowledge about the allegations that have been made, and I stress the word allegations.''
Ms Davidson said: "This morning, Michelle Thomson's solicitor said that she wants to come back into public life as quickly as possible.
"Let's put the police investigation to one side for a moment, on the basics of ethics and integrity alone, does the First Minister welcome Michelle Thomson back to her front bench?''
Ms Sturgeon said: "For the so-called party of law and order to say on extremely serious matters 'let's just put the police investigation to one side' frankly beggars belief.
"I am in no doubt whatsoever in my mind that if the allegations are proven to be correct then that will represent behaviour that I find completely unacceptable.
"But I am not going to judge the outcome, on the basis of someone who maintains their innocence, an investigation that has not yet concluded.''
She added: "When we have all of the facts when the investigation has concluded, I will take whatever decisions and whatever actions I deem necessary, but those decisions will be driven by facts not by insinuation and the attempts of opposition parties to stir up political trouble and difficulty.''
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