In the video, Ms Sturgeon can be heard telling others present at party’s meeting of its national executive committee: “There are no reasons for people to be concerned about the party’s finances and all of us need to be careful about not suggesting that there is.”
Ms Sturgeon, her husband and former SNP CEO Peter Murrell, and former treasurer Colin Beattie were all arrested and questioned as suspects.
READ MORE: Operation Branchform: Complainer demands action on probe
They were each released without charge while the police continue their inquiries.
Mr Murrell and Ms Sturgeon’s home was searched and police are probing hundreds of purchases believed to have been made with party cash.
A source told the Sunday Mail: “The line of questioning has been about what people knew of various purchases, who would have been able to make purchases, and who could reasonably have known about purchases and who would have had access to accounts and spending information.
“The video is of significant interest because detectives have referred to it repeatedly, wanting to know what people who were on the NEC ruling body took from what Nicola Sturgeon was saying.”
READ MORE: Operation Branchform: Police chief rejects attacks on SNP probe
The Operation Branchform probe is focused on how cash raised in 2017 and 2019 as part of a referendum appeal has been spent.
In February last year, Ms Sturgeon announced she would quit as first minister and SNP leader.
Mr Murrell was arrested in April and his and his wife’s home was searched the same day.
Police Scotland officers carried out a search of the SNP’s headquarters in Edinburgh on the same day and also seized a luxury campervan from Mr Murrell’s mother’s driveway in Dunfermline.
Last month it emerged that detectives investigating the SNP’s finances have requested to re-interview staff working at the party’s headquarters.
Workers, including those who were not in place when the inquiry began, have been sent letters asking them to speak to officers. A source said that this move was being directed by the Crown Office, Scotland’s prosecution service.
Separately, The Herald reported on a call by one of the complainers in the case for the investigation to come to a conclusion amid concerns it was dragging on.
The investigation was first launched in July 2021, more than two and a half years ago.
Ms Sturgeon was arrested and questioned for seven hours and then released without charge in June last year.
Mr Murrell has kept a low profile since his arrest.
Ms Sturgeon has continued in her role as an SNP MSP and attended her party’s annual conference in Aberdeen last October.
Colin Beattie, the SNP MSP and former party treasurer, who was arrested two weeks after Mr Murrell, is still visible in the Scottish parliament.
Police were initially asked to investigate whether funds donated to promote a campaign for a new independence referendum were improperly used but the probe has now widened to include potential fraud.
There has been frustration at the top of the SNP about how long the investigation has taken. Senior figures believe it has cast a shadow over the party, undermining trust and damaging their electoral prospects.
There is a fear that it will continue to harm the party’s prospects as a general election approaches.
The SNP has previously said it has been co-operating with the inquiry and will continue to do so.
However the party has also said it is not appropriate to comment on a live investigation.