Mayor Bill de Blasio’s DemocracyNYC project just screwed up so badly that it has puzzled the Board of Elections.

The city BOE fielded at least 1,600 calls this week from long-active voters who’d opened letters from DemocracyNYC warning they might be unable to vote next month. And they were just a fraction of the 400,000 New Yorkers who got the dubious notices.

The mailing cost $200,000, City Hall says, though it has yet to explain how it managed to send it to people who aren’t at risk.

Doug Kellner, co-chair of the state Board of Elections, figures City Hall meant well — but can’t understand how it could “fail to check the accuracy of the voter data it was using.” The state board has now written DemocracyNYC demanding answers — who exactly the city contacted, what’s in the database used by Civis Analytics, the consultant hired to do the mailing, and so on.

Other experts are mystified as to why the letters, dated Oct. 11, went out so close to the Oct. 12 deadline to register to vote and the Oct. 17 one to file a change of address.

City Hall says it’s pushing the Democracy­NYC initiative partly because it lacks confidence in the (bipartisan) Board of Elections to boost turnout. But the city Campaign Finance Board also has a nonpartisan get-out-the-vote effort. Does City Hall secretly think that what’s needed is a partisan drive?

Whatever the motive, it’s impressive that Team de Blasio’s bungling can be as disruptive as Russian hackers trying to mess with US elections.