He was desperate to die — and city health workers did little to stop him.

A suicidal man whom cops had talked off a rooftop Monday was able to get back on a ledge two days later — and jump to his death this time — thanks to a Bronx hospital’s revolving-door policy with mental patients, sources told The Post.

Kareem Cooley, 25, died Wednesday at Lincoln Hospital after his 21-story plunge from 680 Trinton Ave. at the Adams Houses in Mott Haven at 9:30 a.m.

Sources said he never should have been on the streets following his first attempt.

Cops on Monday found Cooley atop a building on East 152nd Street, in the same public housing complex, and spent two hours trying to keep him from jumping. He was finally grabbed by officers and taken to Lincoln Hospital, which is operated by the city Health and Hospitals Corp.

Cooley got a psychiatric evaluation and was released.

The HHC hid behind patient privacy laws when asked why he was allowed to go free without a more thorough examination.

A source at the agency said there is no mandated minimum or maximum period of time required for evaluation or hospitalization because each case is different.

“At HHC patient safety is paramount. This is a tragic event and our hearts go out to the family. Unfortunately, due to patient privacy we are unable to provide any information at this time,” said HHC spokesman Ian Michaels.

Law enforcement sources said Lincoln Hospital is notorious for its lax policies with emotionally disturbed patients — with some released “within hours.”

“There have been cases where patients got out quicker than the cop who brought him in,” a source said. “In one case, they asked the person, ‘Do you want to kill yourself,’ and then when the person said no, they let him go.”

Another police source said, “If the on-call doctor deems a patient a nonthreat to himself or others, they will give them medication and release them.”

Cooley was so determined to die Wednesday, he fought off cops with a stick. “He was more prepared this time,” said a witness, Jonathan Esteva, 31.

On Sunday, Cooley posted a Facebook rant proclaiming he would not “die in vain.”

“This is my last video. These are my last words,” said the aspiring rapper. “Family take care. Everybody take care . . . It’s not like I got family. I’m really by ­myself, and you know this will be the last time you see me.”

Additional reporting by Yoav Gonen