The claims of a Girl Scouts leader that a New Jersey mall crook swiped her troop’s cookie-sale cash crumbled under scrutiny, cops said Wednesday.

Troop 80062 leader Jessica Medina had told cops that on Jan. 18, she placed more than $1,100 in cash and checks from their sale of Do-Si-Dos and Thin Mints at the Woodbridge Center Mall into an envelope — and it was then swiped from their table, robbing the youngsters of funds for a trip to Savannah, Ga.

Medina pointed the finger at a handicapped man and an elderly woman as the thieves — while bringing her 5-year-old daughter out to be photographed tearfully clutching a box of shortbreads.

The story made national headlines and prompted kind-hearted New Yorkers to offer thousands in donations to the troop to make up for the pilfered cash — including from the hosts of TV’s “The Talk.”

But the Woodbridge Police Department on Wednesday said Medina’s tale turned out to be half-baked.

After interviewing the scouts and watching security footage, the cops say no one else in the mall ever saw an envelope on the table — while the cookie dough stayed “secured in a cash box” the whole time.

Police also located the accused man and woman, and eliminated them as suspects.

When they questioned Medina again, she changed her story to say the missing cash wasn’t from the cookie sale after all, but rather “previously submitted by the Girl Scouts to pay for scouting events such as roller skating and the Daddy-Daughter dance” that she was planning to deposit in the bank, the police said in a statement.

When the cops conducted a final interview with Medina, telling her their investigation didn’t support the idea that cookie money had been stolen, they say she “agreed with the findings, speculating that perhaps the envelope containing the money was accidentally discarded with the trash as the scouts cleaned up the area.”

The Girl Scouts of Central and Southern New Jersey said Medina has now been removed from her volunteer position as troop leader.

“We are surprised and very saddened at the turn of events,” Ginny Marino, CEO of the chapter told Patch.

Reached Wednesday, Medina insisted to The Post that she never changed her original story — claiming the cops are blaming her to cover a “bungled” investigation.

“It became the blame game after 12 days of not doing their job properly,” she said. “If they’d found them that night they would have been able to arrest them. That person would have had the envelope in their possession that night.”

She insisted the surveillance footage proves the people she accused did take the cash — but the detectives thought the town would look bad if they “arrested someone with special needs.”

Medina said she had no reason to take the money herself because her husband “makes $200,000 a year.”

“Why would I take a thousand dollars? I’ve got $50,000 worth of cookies sitting in my house right now. I’ve got thousands of dollars of cookie deposits that come in every Thursday,” she said.

She added that the troop never saw a penny from those who offered to donate money — and accused the local chapter of trying to take the pledges for itself.

One good Samaritan who was so moved by the scout troop’s story that he’d offered to donate $1,100 said he never got that chance because the group stopped communicating with him about three or four days ago — but now he’s keeping his money.

“No way. There are so many better things in the world to donate to. I’ll donate to St. Jude’s,” said Paul Bluemke, 49, a retired sanitation worker in Levittown.

“This is why people don’t trust anybody anymore. It’s a shame.”