Murrell was first arrested and questioned in April 2023 under Operation Branchform, a police probe into SNP finances which began more than three years ago.
A year later, he was charged with embezzlement and the Crown Office is currently deciding how the investigation should proceed.
Nicola Sturgeon was also arrested, in June 2023, but was released without charge. She insists she has done nothing wrong.
She had resigned as SNP leader and first minister earlier that year, but has said her decision was not connected to the police investigation.
Colin Beattie, the former SNP treasurer who was arrested under Operation Branchform about a week after Peter Murrell in 2023, has also denied any wrongdoing.
