The 58-year-old was arrested on Wednesday morning in connection with a long-running Police Scotland investigation into the spending of about £600,000 which was earmarked for Scottish independence campaigning.
He was released from custody the same evening “pending further investigation”.
Three police vans were parked outside the couple’s Glasgow home on Thursday morning, with two uniformed officers stationed outside.
A large blue tent remains in place in the front garden of the property, which has been screened off with blue police screens.
The house and garden remain cordoned off with police tape.
Police activity continues at the address with several officers stationed outside and plain-clothes officers seen entering and leaving the property. One was carrying two large rolls of bubble wrap.
One of the uniformed officers was wearing white protective foot coverings while other officers could be seen carrying them after leaving the house.
Ms Sturgeon cancelled a planned appearance at a climate change event in Edinburgh on Thursday evening, with her spokesperson saying she wanted to “keep the focus of the event on the critical issue of the climate emergency”.

1. Officers from Police Scotland outside the home of former chief executive of the Scottish National Party Peter Murrell, in Uddingston
Officers from Police Scotland remain outside the home of former chief executive of the Scottish National Party (SNP) Peter Murrell, in Uddingston, Glasgow, after he was "released without charge pending further investigation", after he was arrested on Wednesday as part of a probe into the party's finances Photo: Robert Perry

2. The blue tent remains
Three police vans were parked outside the couple’s Glasgow home on Thursday morning, with two uniformed officers stationed outside. Photo: PA

3. Officers remain at the scene
A large blue tent remains in place in the front garden of the property, which has been screened off with blue police screens. Photo: PA

4. Officers from Police Scotland outside the home of former chief executive of the Scottish National Party (SNP) Peter Murrell
Officers from Police Scotland outside the home of former chief executive of the Scottish National Party (SNP) Peter Murrell, in Uddingston, Glasgow, after he was "released without charge pending further investigation", after he was arrested on Wednesday as part of a probe into the party's finances. Photo: Robert Perry