Tregoning told police that the man raped her in a field in Franklin County, Pa., held her overnight and released her the next morning.
After investigators confronted her on Monday with discrepancies in her story, she admitted she lied, police said.
"We were able to verify she was not where she said she was. Things were not consistent. It causes a lot of concern for everyone because we had to put in a lot of time and, certainly, people were concerned," Maryland State Police Cpl. George Stottlemyer said.
Tregoning may have concocted the story after she called home from a pay phone in Myersville on the morning of Sept. 23 and learned that her husband had filed a missing person's report with state police, according to authorities.
Stottlemyer attributed the false report to "marital problems" but would not elaborate. Police said Tregoning was in Washington County part of the time she was missing and in Frederick County the rest of the time.
Hagerstown officials expressed relief on Wednesday that such a frightening crime apparently had not occurred.
Hagerstown City Councilman J. Wallace McClure, who publicly questioned the woman's claim last Friday, said he had doubts from the time he learned about it.
"I had a lot of naysayers about my comments but I stood by them, and now I have been vindicated," he said.
Councilman Lewis C. Metzner said he was happy to learn the report ended up being false.
"It's very relieving to know. It was discouraging to hear it even might have occurred," he said.
Metzner also said it lends credibility to city and state police, who were criticized last week for not releasing information about the incident sooner.
"I think people might have criticized them unjustly," he said.
Investigators said they began to suspect Tregoning's story in the days after she reported the incident. Pennsylvania State Police Trooper Mike Gayman said the woman could not remember where the rape supposedly occurred and then skipped a follow-up interview and did not return phone calls.
Maryland State Police Trooper 1st Class Rick Bachtell said the woman gave inconsistent statements last week. He said investigators interviewed witnesses who gave different accounts of where Tregoning went after the rape occurred.
Those statements caused authorities to re-examine the initial report, he said.
"We started feeling there was a chance she wasn't telling us the truth," Bachtell said. "It was not a well-thought-out story."
Stottlemyer said investigators also found inconsistencies between statements Tregoning gave to Pennsylvania and Maryland police. He said police checked to make sure the discrepancies were not the result of a woman who was traumatized.
"We were able to verify that wasn't the case," he said.
Still, Bachtell said the "sensational" aspects of the report led authorities to push other cases to the back burner.
"When there's a report of a carjacking and kidnapping, you have to take that seriously," he said. "It's unheard of (in this area) and if the bad guy's out there, we want to identify who he is."
Bachtell said investigators had begun to do just that. A Frederick County sheriff's deputy who read about the incident in the newspaper called state police officials with a possible lead. The deputy told investigators the report was similar to a case the sheriff's office handled a few years ago.
Bachtell said authorities were preparing a photo lineup for Tregoning to review.
Bachtell estimated that state police in Frederick invested about 50 to 75 hours in the investigation. That time would have a value of at least $1,000, he said. That would not take into account time lost on other cases, he said.
"We're kind of the victims of this in a way," Bachtell said.
Bachtell said prosecutors might seek restitution from the woman. A conviction on a charge of filing a false report is a misdemeanor with a maximum penalty of six months in prison and a $500 fine.
Staff Writer Guy Fletcher contributed to this story.