The SNP must “absolutely get our house in order” and ensure transparency and openness in the party’s governance, Scotland’s Deputy First Minister Shona Robison has said.

She was speaking as police investigations into the party’s finances continued and following the second arrest as part of the inquiry.

Earlier this month, former party chief executive Peter Murrell was arrested and questioned for more than 11 hours before being released without charge “pending further investigation”.

On Tuesday SNP treasurer Colin Beattie was arrested and was also released without charge “pending further investigation” later in the day.

Speaking on BBC Radio Scotland’s Good Morning Scotland programme on Wednesday, Ms Robison said that decisive action is “absolutely critical” and that going forward the governance of the party needs to be “absolutely about transparency, openness”.

Police Scotland have been looking into how more than £600,000 in donations to the party earmarked for an independence referendum had been used.

Asked whether the party is concerned that former first minister Nicola Sturgeon might be arrested she declined to comment on speculation.

She said: “I’m not going to speculate on any of that, I don’t think that would be helpful.

“We need to wait for the facts to be established, whether that’s through the ongoing police investigation and of course the review about how the party is managed and that of course is really, really important not just to reassure party members, but it is important that the public expect us to get our own house in order while also important focusing as a government on supporting their households through the cost-of-living crisis and of course that’s what the First Minister set out yesterday in terms of the policy prospectus.”

Ms Robison said she does not know whether Ms Sturgeon has spoken to police.

Asked whether she has been in touch with the former first minister she said: “What I have done right at the beginning of the process is I sent her a very short message asking after her welfare really and I got a very short reply so we’ve had no discussions whatsoever about the police investigation and it wouldn’t be appropriate for me or her to do so.”

We’ve got to absolutely get our house in order, the public will expect nothing else

Defeated SNP leadership candidate Kate Forbes has told BBC Radio 4 that claims about the party’s finances had been “mind-blowing” and that “decisive and quick action” is needed or the SNP will be in trouble.

Ms Robison told BBC Scotland: “On the decisive action it is absolutely critical, Kate Forbes is right and that’s why of course Humza Yousaf has taken that decisive action by talking about that need for a fresh approach to governance within the party.”

She said that Mr Yousaf has put in place a review of how the party is managed “to ensure that we absolutely get the best governance”.

Asked whether Ms Sturgeon should be suspended from the SNP, Ms Robison said that Mr Yousaf has made it clear that people are innocent until proven otherwise and therefore it would not be appropriate to suspend anyone’s party membership in this situation.

She added: “Going forward, the governance of the party needs to be absolutely about transparency, openness and people should be able to question, and question about the accounts or any other matters, that’s quite right and proper.

“We’ve got to absolutely get our house in order, the public will expect nothing else but meanwhile we also have to address some of those concerns that the public have about other matters like the cost-of-living crisis.”