The Brooklyn EMT who callously refused to help a dying pregnant woman because she was on her coffee break saw her official misconduct charge dropped today after EMS chief Abdo Nahmod — who initially supported the case against her — flip-flopped, leaving frustrated Brooklyn prosecutors no choice but to dismiss the case.

Melisa Jackson, 27, was in uniform and on-duty when she snuck away from her dispatcher job at FDNY headquarters in downtown Brooklyn in December 2009 to meet her EMT boyfriend in a nearby Au Bon Pain. But when pregnant Eutisha Rennix, 25, had a serious asthma attack, Jackson wouldn’t even walk into the back room to look at her.

Both Rennix and her unborn baby died.

“Had the defendant just walked into the rear room, she would have seen that this was not just a person who needed transport to a hospital. Ms. Rennix needed immediate medical assistance,” assistant district attorney Kevin Richardson said in court this morning.

“Ms. Rennix did die that day there on the floor in the rear locker room of Au Bon Pain, and the defendant had her coffee.”

Nahmod signed an affidavit in 2010 supporting the criminal complaint against Jackson. His affidavit said Jackson had violated a departmental rule — the “flag-down rule” — requiring that an on-duty EMT treat a defendant and notify dispatch if they are flagged down for help.

But on Wednesday, Nahmod called Richardson and said the flag-down rule doesn’t apply in this case because Jackson wasn’t assigned to an ambulance or special event where they are expected to provide aid.

“Based on the reversal of position of Chief Nahmod, there is absolutely no possible way to sustain a criminal charge against Ms. Jackson,” Richardson said in court.

“We’re perplexed. We don’t know why he changed his mind,” a law-enforcement source said.

Outside court Jackson refused to apologize to the Rennix family or accept any responsibility — and said she would do the same thing again.

“I had no type of equipment to render aid, because I worked inside of a dispatch center behind a computer,” Jackson maintained – even though she never even stepped into the back room to see what type of help was needed.

“If the same thing happened again, and I worked inside a 911 dispatch center, I would call 911 to have an ambulance dispatched to the location so they would be able to render care.”

jsaul@nypost.com