City inspectors uncovered conclusive evidence of lead paint in 34 public housing apartments where lead-poisoned children were living — but the city failed to force repairs or move the kids out, The Post has learned.

Instead, the Health Department allowed the New York City Housing Authority to appeal the findings, leaving dozens of kids in the tainted apartments and potentially exposing them to further harm for years, official records reveal.

The 34 apartments were the most contaminated of 91 where lead initially was found between 2010 and 2017 after pediatricians reported that one or more children living there tested positive for elevated levels of lead in their blood.

But NYCHA was able to appeal 88 of the cases due to the testing method that was used, and Health Department officials sided with NYCHA in 83 of those cases, overruling their own inspectors.

As a result, likely lead paint was left in all but five of the apartments, the records show.

“It seems especially heinous that the agency that is supposed to be protecting children finds out that children are lead paint-poisoned, finds the apartment has lead and then allows the landlord — a public landlord — to get away with not abating the lead,” said Legal Aid lawyer Judith Goldiner, who has repeatedly filed suits over NYCHA’s substandard living conditions.

“This means a kid that has already been poisoned could get worse and that other children that come to that apartment could be poisoned.”

Details of the lead paint testing were contained in nearly 4,500 pages of internal Health Department inspection reports obtained by The Post through the Freedom of Information Law.

They were made public amid a spiraling scandal over lead paint that began in late 2017 when the Department of Investigation revealed that NYCHA covered up years of failure to comply with federally required lead checks.

The fallout forced the resignation of Mayor Bill de Blasio’s NYCHA chair, Shola Olatoye, and led the authority to spend $88 million on lead testing that is underway in 135,000 of its 174,000 apartments.

“The Health Department is only going in after these kids have been poisoned,” said lawyer Matthew Chachere of the nonprofit Northern Manhattan Improvement Corp., who helped write the city’s lead laws.

“It’s their job to make sure these kids are no longer at risk, and these findings raise serious questions about if they’ve abdicated that responsibility.”

Lead exposure, primarily caused by peeling paint, can cause brain damage and other health problems. The federal Centers for Disease Control and Prevention warns that any amount can be dangerous to young children.

When blood tests show a child has been poisoned, the Health Department sends an inspector to their apartment to check for lead.

In 88 of the 97 inspections at the 91 apartments, the inspectors used X-ray guns — known as XRF devices — to check peeling paint and other surfaces for lead.

Under city rules, any measurement of 1 milligram of lead or more per square centimeter (less than ¼ of a square inch) of paint mandates removal and replacement or repair of the paint.

Results that fall within the XRF’s 0.3 milligram margin of error must be double-checked through lab analysis, but any reading of 1.3 milligrams or above is considered conclusive proof.

The records obtained by The Post show inspectors found at least one reading above the 1.3 milligram threshold in 34 of those apartments, or two out of every five apartments where lead was found.

NYCHA contested every one of the readings and persuaded the Health Department to partially or completely retract its lead paint removal orders in 33 cases.

The sole removal order occurred in 2010 because NYCHA failed to file any paperwork to support its appeal.

Dr. Morri Markowitz, who heads the lead program at the Children’s Hospital at Montefiore Medical Center, said he couldn’t understand why the Health Department didn’t trust its own findings.

“Your inspectors found potential lead hazards contributing to elevated blood lead level in a kid living in that apartment,” he said.

“NYCHA contested your result. Why did you believe the NYCHA result over your own?”

The Post’s examination also revealed that the Health Department sided with NYCHA in nine of the 34 cases despite the housing agency’s own tests showing substantial evidence of lead.

In 2017, NYCHA filed a report with one appeal that disclosed its own paint chips tested positive for lead amounts just shy of the legal threshold — including readings of 0.85, 0.91 and 0.99 milligrams of lead.

The Health Department did not require repairs.

“It’s another example of how the city fails to enforce its own laws,” said Reuven Frankel, an attorney with a history of filing lead-related suits against NYCHA.

“If a child ingests that paint-chip sample, there’s no competent physician who would say that that would not be a health hazard. On the contrary, it should confirm the need to commence remediation.”

Neither the Health Department nor City Hall disputed any of The Post’s findings.

“We’ve significantly reduced lead exposure for kids in public housing, and now we’re taking action to eliminate it altogether,” said mayoral spokeswoman Marcy Miranda.

“NYCHA now immediately abates any apartment the Health Department identifies.”

Additional reporting by Bruce Golding