The party was rocked this week when the Glasgow home shared by its former chief executive and Nicola Sturgeon was searched by officers for two days.
Murrell was arrested on Wednesday morning and questioned for several hours before being released without charge.
The SNP head office in Edinburgh was also searched on Wednesday.
Police Scotland has led a longrunning investigation into SNP finances after several complaints were made in 2021 regarding a fundraising drive for independence campaigning.
Accountancy firm Johnston Carmichael has now ended its decade-long business relationship with the party after reviewing its client portfolio.
BBC Scotland reported the decision was made before Murrell was arrested this week.
An SNP spokesman said: "We can confirm that Johnston Carmichael will not be providing audit services to the SNP this year.
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