IT was lucky for Nicola Sturgeon that Tuesday’s meeting of Holyrood was a wholly online affair. The First Minister, broadcasting from the inky gloom of something akin to Darth Vader’s sarcophagus, was thus able to stay focused on the latest Covid update.

Had she set foot in parliament, it would have been a very different story.

There, she would undoubtedly have been doorstepped by the media and diverted onto the breaking news about Police Scotland launching a formal investigation into SNP fundraising.

No small matter, especially as the SNP’s chief executive is Ms Sturgeon’s husband, Peter Murrell.

As I’ve written here before, I am very doubtful that this will end in a criminal conviction. Time will tell if I’m right or a chump on that score. However for any party, and particularly a party of government, to be the focus of a criminal inquiry looks appalling.

Only last month Ms Sturgeon insisted there was nothing to see here.

“I’m not concerned about the party’s finances,” she told STV News after five SNP office bearers resigned complaining about a lack of financial transparency.

They included the treasurer, the MP Douglas Chapman, something a mere mortal might have felt was a red flag.

Well, Ms Sturgeon had better be concerned about the money now, because this is going to stink up the SNP for the foreseeable future.

To recap, in March a member of the public went to the police alleging fraud based on the party soliciting funds for a second referendum campaign, then spending it on other things.

Some £665,000 has been donated specifically for Indyref2 since March 2017, when Ms Sturgeon announced plans for a new vote on the back of the Brexit referendum, only to be wrongfooted by SNP losses in the snap general election a few weeks later.

After she announced a long “reset”, the campaign ardour fizzled out.

Cash supposedly ringfenced for Indyref2 appears to have been applied to more pressing party needs, possibly including the repayment of loans.

New treasurer Colin Beattie MSP - actually the old treasurer brought back after Mr Chapman quit - now promises that a sum “equivalent” to the money raised, though not the original pot of donations, will be found for Indyref2 campaigning when the times comes.

The police took three months to assess whether a full investigation was merited, as publicity around the first complaint attracted another half-dozen, adding to their work.

After consulting with prosecutors, the police have now moved up a gear, launching an investigation proper, and have asked anyone with information which might help to come forward.

Given the time taken to assess seven complaints, it’s a far bet investigating still more will take us into next year.

That means a drip-drip of stories as Mr Murrell, the auditors, and others are quizzed about the accounts.

Even if the police do conclude something is awry, there is no guarantee the Crown Office would decide to prosecute or, if there was a prosecution, that it would succeed.

The SNP can argue everything it does and all it spends is directed towards independence, and whether it was that pound over there or this pound over here is immaterial.

But even if the party is blameless, the process alone is a big problem for it.

It is a grinding, enervating burden and a gift to the SNP’s opponents, who will encourage voters to see the police’s involvement in and of itself as evidence of skulduggery.

As well as the cloud hanging over the party, there is also one inside it.

The police complaint has its origins in a pre-election effort by more gung-ho parts of the Yes movement to tarnish the SNP and push its supporters towards Alex Salmond’s Alba party.

The row over the Indyref2 money, which has been rumbling on for years, was ramped up and weaponised.

However it was never just about proper bookkeeping. It was far more about what the money was for.

It was meant to be spent on a campaign for independence. That it wasn’t being spent on Indyref2 was what struck critics as truly criminal.

Better, they argued, to have someone keen like Mr Salmond in charge than the fainthearts of team Sturgeon.

These promoters of the “missing funds” theory now feel vindicated by the police investigation and will increase their criticism of the First Minister’s slow crawl to freedom.

They may well find an audience. For there is angst among Yes supporters that four years after Ms Sturgeon and her husband asked for it, that money has still not been used in a referendum that seems as distant as ever.

There is still no answer to London’s veto, still no updated independence prospectus, and still, to some eyes, no real appetite for forcing the issue.

Yes, there has been Covid, but that point doesn’t address the wider concern about inertia and a sense that complacency has taken hold.

The probe also foregrounds the surpassing weirdness of a husband and wife duopoly ruling the party, and the self-defeating secrecy which helped fuel rumours of malpractice.

As she took questions from MSPs on Tuesday, Ms Sturgeon wished Willie Rennie good luck as he stands down as Scottish Liberal Democrat leader.

“Ten years is a good shift,” she said. It was hard not to imagine her own shelf life flashing through her mind.

If a decade is a good shift for a minor opposition leader, it’s an epic slog for a premier. She is already seven years in.

A criminal investigation and its distractions make her job even harder, the urge to call time ever greater.

The police complaint may well peter out yet succeed in its original aim - hastening a change of SNP leadership in favour of one demonstrably hungrier for independence.