A $77 million cash infusion from the state to flood the subway system with extra NYPD cops has already run dry — forcing the Mamdani administration to cover the added patrols, The Post has learned.

The state fund — touted by Gov. Kathy Hochul last December as a way to keep a surge of uniformed officers in the subway system — was zeroed out by July, mere weeks into the Big Apple’s fiscal year, city and state officials confirmed.

Mayor Zohran Mamdani, a socialist who campaigned on eliminating police overtime altogether, will now have to honor a deal inked by his predecessor Eric Adams to continue the flood of extra cops in the transit system as…

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