The pair locked horns over the Justice Secretary Michael Matheson, with Ms Davidson questioning a lack of transparency in his work with the police oversight body.
In a separate Holyrood debate, the Scottish Tories demanded a “full and independent investigation” into Mr Matheson’s invention in a decision of the Scottish Police Authority to reinstate Chief Constable Phil Gormley despite bullying allegations against him.
The Tories’ motion said Mr Matheson had “not acted transparently or openly” after his meeting with the SPA had not been minuted.
Ms Davidson raised the issue once again in FMQs, asking Ms Sturgeon whether the real truth behind the issue had been revealed.
The Scottish Tory leader said her counterpart said nine times that Mr Matheson only asked questions of then SPA chair, Andrew Flanagan.
She says Mr Flanagan told MSPs, earlier this morning, Mr Matheson had told him the SPA had made a “bad decision”.
Ms Davidson added: “Here is the most damning thing of all, it is now, on January 25, we are still having to piece together the details of what happened at the beginning of November, when this Government was involved in one of the most important policing decisions it has taken since coming to office.
“Only now are we getting formal evidence that the Justice Secretary was instrumental in preventing the chief constables return.
“But if it hadn’t been for reports in the press, the whole thing would have been kept under wraps and this parliament would have been kept in the dark.”
Responding, Ms Sturgeon said: “On this issue about what parliament knows, there is nothing Ruth Davidson has brought to parliament today that is different to what she brought to parliament last week…”
At this point, Ms Davidson and the Scottish Tory benches exploded with laughter, with Mr Davidson leading the mockery of the SNP.
The First Minister added: “There is nothing in what we heard this morning that changes what is already known because the Justice Secretary came to this parliament and gave a full statement and answered questions from across the chamber on exactly what had happen.”