Gov. Kathy Hochul rushed to the microphones Tuesday to reassure New Yorkers following the Brooklyn subway shootings. She should’ve stood in bed.

Out tumbled a jumble of half-thoughts, unfocused and haltingly delivered, underscoring what has been apparent for some time now — which is that New York’s latest accidental governor would be out of her depth in a Buffalo mud puddle.

Which, in a manner of speaking, is where she came from.

Hochul’s horrible day also included news that her handpicked, staunchly defended lieutenant governor, Brian Benjamin, had just been arrested on federal corruption charges. Benjamin would be gone by day’s end, of course, but the matter will linger.

Actually, the scandal could have been predicted by anybody who pays even cursory attention to New York politics. But Hochul, it seems, doesn’t pay attention to much. This would explain her selection of Benjamin in the first place — and the amazingly ineffective state budget cycle that she just stumbled through.

It would also explain, if that’s necessary, why Gov. Andrew Cuomo brought her on to his ticket in 2014 — him having a thing for dim-bulb staffers. (Cuomo’s history now — probably — but he’s got to be laughing up his sleeve today.)

First, though, the subway shootings press conference — a performance that challenges the ability of mere words to describe, though not to worry: It’ll be coming soon to campaign commercials near you.

Much more substantive, of course, is the matter of how Benjamin became the Empire State’s lieutenant governor. A ham-and-egg backbench state senator from Harlem, the fellow has long carried the odor of petty corruption that permeates official Albany, the Legislature in particular.

But he had the rhetorical chops to appeal to Hochul — just elevated to the executive chamber, in need of a lieutenant governor and looking at primary challenges from New York’s increasing radical left. Who better to raise up than a black, vocal defund-the-police progressive?

So that’s what Hochul did.

Imagine her chagrin Tuesday when she learned that Benjamin had been arrested on federal bribery, conspiracy and related wire-fraud charges following his indictment by a federal grand jury. 

Worse, it was no secret that the feds had him in their sights all along, even if the particulars weren’t well known — yet Hochul not only picked him to run with her for a full term, she firmly defended his place on the ticket until Tuesday.

Loyalty in politics is laudable, if rare. But if there ever were a mistaken judgment that could have been rectified with a discreet dismissal and a “Thank you for your service,” it was this one.

Now Benjamin is gone, except that he’ll apparently be on the June primary ballot anyway — a continuing embarrassment to Hochul and the party in general.

Savvy politicians don’t get themselves in the soup like this — which again amplifies Kathy Hochul’s startlingly thin resume. Service on the Hamburg, NY, town board and a term filing legal documents as Erie County clerk isn’t exactly job prep for the Empire State’s top elected office.

But maybe more to the point, Benjamin’s arrest is sure to focus attention on Hochul’s own ethics issue — her husband.

William Hochul, a career federal prosecutor with no particularly relevant experience, became general counsel to a Buffalo gambling and entertainment company, Delaware North, less than one year after Kathy Hochul became lieutenant governor. This may have been a coincidence, if one believes in them, but the fact is that Delaware North has spent hundreds of thousands of dollars lobbying Albany since then — including the lieutenant governor’s office itself.

Caesar’s wife, please forgive the obvious cliché, hasn’t been a consideration in New York politics for a very long time — if ever. But the utility of being above suspicion — given the Benjamin arrest and the various Cuomo administration corruption scandals — should be clear to all.

So while there are obvious issues with the governor’s overall competence — she was just rolled for billions during budget negotiations, getting very little that’s obvious in return — Tuesday brought her lack of sound judgment into focus.

Also, her inability to speak coherently in a crisis. All in all, Kathy Hochul had a very bad day indeed.