NYCHA chair Shola Olatoye declared this Chelsea public housing complex had been inspected for lead paint. In reality, it had not. Richard B. Levine/Alamy

It remains absurd that Shola Olatoye has not lost her job as chair and CEO of the New York City Housing Authority. Like her predecessor under Michael Bloomberg, John Rhea, she has failed to adequately wrangle with the city within a city. The revelation last year that NYCHA was not performing inspections for lead paint as mandated by federal and city law should have been enough to drive Mayor Bill de Blasio to sack her.

For whatever reason, he hasn’t, even after Olatoye lied to the City Council about the level of certification NYCHA workers had when they inspected apartments for lead paint. When the postmortems on de Blasio’s two terms are eventually written, they will note how the great liberal mayor who so badly wanted to find himself in bronze next to LaGuardia could not rescue the city’s crumbling public housing.

Understandably frustrated, the City Council is now casting about for a new solution: state intervention. Last week — following a winter of broken boilers that the mayor seems to be in no hurry to repair — a number of councilmembers gathered together and called upon Governor Andrew Cuomo to declare a “state of emergency” and rescue the housing authority.

“The state could declare a state of emergency to allow for expedited bidding and contracting with outside companies,” Brooklyn councilmember Robert Cornegy said at a press conference on the steps of City Hall last week.

Such a declaration would not amount to a full state takeover of NYCHA, though the councilmembers would be happy to cede city control for state oversight if all the management ills of the housing authority suddenly disappeared. Naturally, Cuomo has been receptive to the idea of gaining even more power over a city entity: His chief counsel, Alphonso David, signaled openness to declaring an emergency.

But what will actually happen? And how meaningful will this declaration be?

It’s worth noting that Cuomo declared a state of emergency for the subway system last summer. Nothing much has changed, other than the MTA fudging stats over the number of delays and maintaining its nebulous performance metrics. No attempt has been made to reform the transportation authority’s profligate and quasi-corrupt spending practices. Trains still don’t show up when they’re supposed to.

Part of the problem is how little input the city gets in MTA decision-making. Cuomo appoints a plurality of board members and has the de facto power to greenlight or kill projects at will. On a whim, he can shut the whole system down for a snowstorm. He can decree putting lights on a bridge, peculiar towers outside of tunnels, or WiFi in every subway station, finally freeing straphangers to complain about their commutes on Twitter in real time.

Would a state of emergency for NYCHA result in something more? The state, which has fantastically mismanaged the MTA, would ultimately be expected to solve the vexing problems of a public authority that houses 400,000 people — a midsize city’s worth of residents, most of them low-income.

If a state of emergency declaration could expedite boiler repairs and streamline management, all the more power to it. Yet it’s hard to see how a Cuomo administration that once threatened to slash almost a half-billion dollars from CUNY’s budget and can’t even grant New York City the right to pick a single firm to design and reconstruct the Brooklyn-Queens Expressway would suddenly become an enthusiastic, long-term steward of our public housing.

Better management will only do so much, particularly when Donald Trump wants to slash and burn NYCHA’s operating budget. What both de Blasio and Cuomo have to recognize is that the era of federal largesse is long, long over, and any serious rescue of public housing will have to be a city-state joint effort.

Cuomo will have to stop catering to suburban and rural moderates and put up far more in state cash than he ever has before to right NYCHA. De Blasio will certainly have to increase the city’s contribution. He’s right to resist funding the MTA’s pitiful “action plan” — the MTA is a state-run authority and city residents fund it copiously through taxes and tolls — but public housing is another story entirely. It is the city’s responsibility. Whatever is left of the buck stops at City Hall.