The Scottish Labour leader said she had “zero recollection” of approaching the SNP but declined to categorically rule out that she had not when making job applications 13 years ago.
Reports suggested that Ms Dugdale had emailed Richard Lochhead, the long-serving SNP MSP and rural affairs secretary asking to be considered for a job as a researcher when she was sitting her law finals at Aberdeen University.
On Wednesday The Liberal Democrat leader Willie Rennie called on the Information Commissioner’s Office (ICO) to investigate whether details of the alleged application had been released by the SNP.
In a letter to the ICO, Mr Rennie said that if private information concerning Ms Dugdale and the SNP had been made public it would amount to a “serious breach of data protection”.
On Wednesday night the ICO said it would act if it found evidence that personal information had not been kept securely.
After the claims about Ms Dugdale’s actions as a student were reported in a tabloid newspaper on Wednesday, the SNP denied that any documents had been passed to an outside organisation.
Ms Dugdale was asked about the claims when she attended a lunch hosted by the Scottish Parliamentary Journalists’ Association on Wednesday.
When asked if she had ever supported the SNP, she replied: “No.”
The Scottish Labour leader said: “I think this is the beginning of a dirty tricks campaign during this election campaign. Why is that happening? Because I am the only one in this election prepared to take on the big issue of how we stop the cuts and end austerity in Scotland. The SNP are prepared to match that commitment or really take it on and talk about it on their own terms, so they have decided to come after me instead.
“I have supposedly applied for work experience 13 years ago in February 2003. I have absolutely zero recollection of this. I was a law student at the time. I was studying for my finals. I find the whole thing just a complete anathema.I don’t know where it has come from.”
Ms Dugdale said she had not seen the details of her alleged job application, so was “unable to verify it or otherwise”.
She added that young people considering work experience with the SNP to boost their career should now be “really worried ... that it might bite them” in the future.
Mr Rennie’s call for an ICO investigation was backed by Labour’s shadow Scottish secretary Ian Murray.
The Lib Dem leader’s letter to the Assistant Commissioner for Scotland and Northern Ireland, Ken Macdonald, said: “Reports in the media today have focused on an application from the Scottish Labour leader Kezia Dugdale for employment with the Scottish National Party over ten years ago as she was finishing university.
“Speculative applications for employment are often made with data frequently kept on file by employers for some time afterwards.
But that application should have remained confidential and I believe that if it was released by the SNP to a journalist it amounts to a serious breach of data protection.”
Mr Rennie added: “Scots deserve to know that employers collect, use and keep personal information appropriately and I would invite you to investigate this matter as I am deeply concerned about the implications for civil liberties in this country.”
An ICO spokeswoman said: “We’re aware of this story. The law requires organisations to keep personal information secure, and to not keep it longer than is necessary. We’ll act where we see clear evidence that this hasn’t happened.”
Ms Sturgeon said the story was “probably more light-hearted than anything else”.
She said: “I think young people, if they have got an interest in politics, regardless of their party affiliation, should be encouraged to get involved and get experience.”
A SNP spokesman said: “Why the Lib Dems are being so po-faced about a light-hearted story which has already been laughed off by Kezia Dugdale is anyone’s guess.
“It’s clear they’ve resorted to diversionary tactics since they can’t win votes on their deeply flawed policies. The fact Ms Dugdale asked for a position in the SNP has been very common knowledge in Holyrood circles for a long time. No documents of any kind have ever been given to any outside organisation.”