The SNP leader hit out after Theresa May claimed that the nationalists had been fined for mistakes on election expenses.
But Ms Sturgeon insisted her party “always played by the rules” in elections, as she accused the PM of trying to distract attention away from questions over Tory expenses in the last general election campaign.
The Crown Prosecution Service (CPS) said on Wednesday that even though spending returns submitted by some of the party’s candidates and officials may have been inaccurate, there was insufficient evidence to prove they were knowingly dishonest.
The Tories have already been fined a record £70,000 by the Electoral Commission for ‘’numerous failures’’ in reporting their expenses for the 2015 general election and three by-elections in 2014.
Mrs May insisted Conservative expenses were “properly reported and properly declared and that the candidates did nothing wrong”.
She said: ‘If you look at the expenses issue, we have seen all the major parties and the Scottish nationalists being fined for mistakes made on national expenses. We have paid our fines and I sincerely hope the other parties are paying theirs.’’
Ms Sturgeon called on the Prime Minister to “apologise for attempting to smear the SNP”.
The SNP leader said: “Yesterday we saw the Crown Prosecution Service say that they couldn’t prove criminal intent on the part of Tory candidates, but clearly saying like the Electoral Commission had already done, that there were likely to have been errors in Tory election expense returns.
“Not to put too fine a point on it I think there is some evidence that Tories at the last general election were not playing by the rules and for Theresa May to try to distract attention from that by smearing other political parties I think is unacceptable - for anybody but particularly for the Prime Minister.
“The SNP unlike the Tories has always played by the rules in elections and we have never been fined by the Electoral Commission.
“I’ll give Theresa May the benefit of the doubt that she just made a mistake but either way I think we should see a retraction and an apology from her for smearing the SNP in the way that either intentionally or inadvertently she did yesterday.”