City correction brass violated the Big Apple’s controversial “sanctuary city” rules by allowing a department investigator to tip off the feds about illegal immigrant inmates, a scathing new report said.

The Department of Correction dropped the ball when it let the staffer, who was not identified, tell US Immigration and Customs Enforcement officials that illegal immigrants were being released, allowing the feds to nab them for deportation, a Department of Investigation report said Thursday.

The move — which officials said was done “unwittingly” — violated city law that bars cooperation with ICE on civil deportation cases. 4

“New York City law and DOC policy do not allow city resources to be used for the purpose of facilitating the enforcement of federal immigration law, and that

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