Former SNP chief executive Peter Murrell was last night released without charge by the police, pending further investigation into party finances.
Mr Murrell, 58, the husband of ex-first minister Nicola Sturgeon, was arrested on Wednesday morning.
He was questioned while police searched their Glasgow home and SNP headquarters as part of their investigation.
Ms Sturgeon said she had "no prior knowledge" of Police Scotland's plans.
The force said inquiries were ongoing.
In a statement, Police Scotland said Mr Murrell was arrested at 7:45am and released shortly before 7pm.
Searches
"Officers also carried out searches today at a number of addresses as part of the investigation," the statement added.
"A report will be sent to the Crown Office and Procurator Fiscal Service."
Mr Murrell resigned as SNP chief executive last month, after holding the post since 1999.
He has been married to Ms Sturgeon since 2010.
A spokesperson for her told the BBC she was not warned about Police Scotland's action or intentions before the arrest.
They added: "Ms Sturgeon will fully co-operate with Police Scotland if required, however at this time no such request has been made."
'Difficult day'
Ms Sturgeon was succeeded last week as first minister by Humza Yousaf. Following Mr Murrell's arrest, Mr Yousaf said that it was "a difficult day" for the SNP. He said his party had "fully co-operated" with police and would continue to do so.
Police activity continued at the Glasgow home of Mr Murrell and Ms Sturgeon on Wednesday evening.
Ms Sturgeon had been inside the house when officers arrived to make the arrest.
The house was sealed off with blue and white tape. A tent was erected on the driveway with a van parked inside.
Officers could also be seen searching a small shed and storage box in the back garden.
In Edinburgh at least six marked police vehicles were parked outside SNP HQ and officers carrying green crates and other equipment were seen going inside.
In July 2021, Police Scotland launched a formal investigation into the SNP's finances after receiving complaints about how donations were used.