Hillary Clinton’s campaign and its supporters are linking Donald Trump to President Vladimir Putin. This must make the Russian President chuckle. After all, he accused Clinton of inciting protests in Moscow in 2011.

The Democrats, however, need a reality check. The suggestion of a Russian connection to the Trump campaign is unfounded, at best. And although the hack of the Democratic National Committee’s servers, the spoils of which were recently posted on WikiLeaks, was probably the work of Russian hackers, no one is denying that this operation exposed an embarrassing tilt of the party in favour of Clinton and against Bernie Sanders.

Clinton’s campaign manager, Robby Mook, said on CNN that he saw a link between the release of the hacked DNC e-mails just before the Democratic convention and the Trump campaign’s successful effort to remove from the Republican platform an amendment calling for “providing lethal defensive weapons” to its military.

“I think when you put all this together, it’s a disturbing picture,” Mook said.

At the same time, liberal blogger Josh Marshall wrote a lengthy post about alleged links between Trump and Putin, including the Republican nominee’s dealings with wealthy Russians.

There is plenty to “put together” to make it look ominous. Besides, as Marshall correctly pointed out, Russia’s state-owned media have been openly rooting for Trump. But is there a real Putin-Trump connection and enough evidence to say that Trump is accepting help from Putin? I don’t think so.

Trump has not been linked to any official or businessman close to Putin’s inner circle. The Trump Soho project apparently received funding from Iceland’s FL Group — now known as Baugur — which had some Russian investments but no known ties to Putin’s friends. He also has links to Alexander Mashkevich, a wealthy businessman from Kazakhstan.

Mashkevich is not part of Putin’s circle of billionaire cronies. Similarly, the business dealings in Ukraine of Trump’s campaign manager, Paul Manafort, have raised eyebrows, but none involved Putin’s friends, and one businessman with good Kremlin ties — but not from the inner circle, either — (Oleg Deripaska) has been trying unsuccessfully to get some money back from Manafort and his partners.

It is worth remembering, too, that Ukraine and Kazakhstan are not part of Russia. Their business elites are similarly corrupt, but Putin is not the source of their wealth, which they have used to buy expensive real estate of the kind that Trump has developed.

The only Trump policy adviser with real ties is Carter Page, who advised Gazprom, the Russian natural gas monopoly, in the mid-2000s. These connections, however, are not at the highest level: Page is not pals with Gazprom chief executive officer Alexei Miller, who is close to Putin.

Put together, this appears no more damning than Clinton’s tenuous “Russia connection” — the big donations to her family foundation from investors in a uranium company whose sale to Russia’s state-owned Rosatom needed a sign-off from the US Government. There is no evidence that Clinton, who was Secretary of State at the time, lobbied in favour of the deal or helped to get it approved. And Rosatom itself — an arm of the Russian Government — did not pay anything to the foundation.

The former Soviet Union is a big place, and a lot of business is being done there. It should not be surprising that people in the upper echelons of American business and politics have connections to that part of the world. Unless these ties are to a dozen specific individuals whom Putin has made super-rich in his 15 years in power, they are not politically significant.

The Russian connection in the DNC hack is stronger, but has not been proved — the FBI said yesterday that it had opened an investigation. CrowdStrike, the security firm hired by the DNC, has linked the tools used to two well-known groups that operate on Russian time, keep regular hours and that use Russian versions of certain software. Besides, there is independent confirmation that the leaked documents were processed on machines using the Russian language.

The hacker calling himself Guccifer 2.0, who claimed to have stolen the documents, said he was from Romania but had a hard time conversing with an interviewer in Romanian.

It is probably enough to go on for tentative attribution — ThreatConnect, the cyberthreat intelligence company, has provided good analysis on the subject.

I have no doubt that Putin would like Trump to win. The Republican candidate has called into doubt America’s commitment to its Nato obligations and even suggested that he may not defend alliance members if they are attacked by Russia. Even so, despite the rumours, there is no credible evidence of a connection.

For now, the Russia story is being used to deflect attention from the turmoil within the Democratic camp. There is no doubt that DNC officials who, in the midst of a storm over Clinton’s use of a private server while Secretary of State, failed to secure their own network, apparently letting in more than one hacker team.

The uproar also takes the focus away from the broader failings of the Clinton campaign, which is even in the polls with a rival who has offended almost every kind of voter, has managed a cheap, disorganised candidacy and has been caught lying.

If Clinton cannot beat Trump, it’s not Putin’s fault, although it would certainly make him happy.

•Leonid Bershidsky, a Bloomberg View contributor, is a Berlin-based writer