Peter Murrell, 58, was taken into custody on Wednesday April 5 and is being forcibly questioned as a suspect as part of the ongoing investigation.
Officers are also conducting “multi-direction” searches.
A report will be sent to the Crown Office and the Solicitor’s Fiscal Service.
A statement from the force added: “The matter is active for the purposes of the Contempt of Court Act 1981 and therefore the public is advised to use caution if discussing it on social media.
“As the investigation is ongoing, we cannot comment further.”
Murrell resigned as CEO during the recent leadership campaign.
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The SNP said it continues to “fully cooperate” with police following the arrest of the party’s former chief executive.
He said: “Clearly it would not be appropriate to comment on any live police investigation, but the SNP has been fully cooperating with this investigation and will continue to do so.
“At its meeting on Saturday, the SNP’s governing body, the NEC, agreed to a governance and transparency review, which will take place in the coming weeks.”