The Crown Office was told on 20 March that Police Scotland wanted a search warrant.

It was not until 3 April - a week after the SNP leadership contest ended - that the application for a warrant was approved by a sheriff.

Officers searched the home of the former first minister two days later.

Details were released by Police Scotland in response to a Freedom of Information Request (FOI) by the Scottish Conservatives that was first reported by the Scottish Sun.

Sources close to the inquiry have denied that there was an undue delay.

But opposition parties said the revelation would "raise eyebrows" and questioned the role of Lord Advocate Dorothy Bain KC, who heads the Crown Office but is also a Scottish government minister.

A spokesman for the Crown Office and Procurator Fiscal Service said: "In all matters, Scotland's prosecutors act independently of political pressure or interference."It is standard that any case regarding politicians is dealt with by prosecutors without the involvement of the Lord Advocate or Solicitor General."

BBC Scotland understands that a draft search warrant was submitted by the police which the fiscal then discussed with officers before its contents were finalised.

The warrant, which is reported to have included a long list of items the police wanted to seize, was then signed by a sheriff on the same day it was finished.

Mr Murrell, who had quit as the SNP's chief executive on 18 March, was arrested when officers investigating the party's finances arrived at the Glasgow home he shares with Ms Sturgeon early on the morning of 5 April.

Several boxes of evidence were removed from the SNP's headquarters in Edinburgh

Police spent two days searching the house, with several boxes of evidence being removed. Mr Murrell was released without charge pending further investigations.

The SNP's headquarters in Edinburgh was also searched on 5 April and a luxury motorhome that sells for about £110,000 was seized from outside the home of Mr Murrell's mother in Dunfermline.

Colin Beattie, who was the party's treasurer at the time, was arrested on 18 April before also being released without charge while further inquiries were carried out. He subsequently quit as treasurer.

The contest to succeed Ms Sturgeon as SNP leader and Scotland's first minister had ended on 27 March when Humza Yousaf, who was the party hierarchy's preferred candidate, narrowly defeated Kate Forbes.

Newspaper reports earlier this year claimed that some people within Police Scotland were frustrated by the direction they were being given by the Crown Office on the SNP investigation.

Scottish Conservative MSP Russell Findlay told BBC Scotland: "There has been this continual sense of something not feeling quite right and of some frustration being expressed not by journalists, not by politicians, but by police officers and this latest revelation perhaps only feeds into that sense.

"From what I understand the Crown Office is suggesting this was perfectly regular and routine, but the entire investigation is so sensitive and is subject to a huge amount of speculation and the more transparency there is around it the better."

'Interesting revelation'

Mr Findlay said the case also raised "fundamental questions" about the role of the Lord Advocate, who heads the independent prosecution service while also sitting as a minister in Scottish government cabinet meetings.

He added: "It doesn't feel appropriate. And that separation needs to happen."

Jackie Baillie, the deputy leader of Scottish Labour, said the two-week delay was a "very interesting revelation that will lead to raised eyebrows across Scotland".

She added: "While I accept that the Lord Advocate may not have had a direct influence on the timing, this story underlines why we need to have a serious discussion about separating the role of the Lord Advocate to ensure that no perception of conflict of interest can ever occur."

Police launched their Operation Branchform investigation almost two years ago after receiving complaints about how a total of £666,953 donated to the SNP by activists was used.

The party pledged to spend the funds on a future independence referendum. Questions were raised after its accounts showed it had just under £97,000 in the bank at the end of 2019, and total net assets of about £272,000.

Last year it emerged Mr Murrell gave a loan of more than £100,000 to the SNP to help it out with a "cash flow" issue after the last election.

The party had repaid about half of the money by October of that year. It still owes money to its former chief executive, but has not said how much.

Ms Sturgeon has previously said the police investigation played no part in her decision to announce on 15 February that she was standing down as SNP leader and first minister.

She also said the first she knew that the police wanted to search her home and arrest her husband was when detectives arrived on her doorstep.

She added: "There are many questions that I would want to be able to answer and in the fullness of time I hope I will answer, but it would be wrong and inappropriate for me to go into any detail of what the police are currently investigating."