“The woman is in custody and is being questioned by Police Scotland detectives,” the force said.
The BBC and other media outlets identified the arrested woman as Sturgeon. The party did not immediately comment.
Scottish police have been investigating how £600,000 ($1.2 million) designated for a Scottish independence campaign was spent.
Party treasurer Colin Beattie and former chief executive Peter Murrell were arrested previously and questioned as part of the investigation. Neither has been charged.
Murrell is Sturgeon’s husband, and police searched the couple’s home in Glasgow after his arrest in April.
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She said that it was the right time for her, her party and her country to make way for someone else.
Sturgeon left office amid divisions in the SNP and with her main goal — independence from the UK for the nation of 5.5 million people — unmet.
Scottish voters backed remaining in the UK in a 2014 referendum that was billed as a once-in-a-generation decision.
Sturgeon’s departure unleashed a tussle for the future of the SNP amid recriminations over the party’s declining membership and divisions about the best path towards independence.
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