Two young cousins who made up a story about being kidnapped after violating their curfew have turned themselves in and are being charged with filing a false report.

Lampasas County authorities had issued warrants against Sasha Abney, 21, and her cousin Bryshada Ward, 18, charging them with making a false report to a peace officer. That's a misdemeanor punishable by up to six months in jail and a $2,000 fine.

Abney and Ward, both of Terrell, Texas, made up the story and hid for four nights because they were afraid of getting into trouble for missing their curfew after a night of partying, FOXNews.com has confirmed.

The search for the girls and the investigation into their alleged abduction involved four different police jurisdictions in Texas.

Ward and Abney left their homes in Terrell, east of Dallas, on Friday night, saying they were going to a movie in nearby Mesquite. One of them then made a cell phone call to a friend at 4 a.m. Saturday and screamed, "Please help!"

The call was traced to an area of Dallas, prompting a police search there that included a helicopter and trained dogs. But the two didn't resurface until Tuesday night when they showed up roughly 150 miles away at a Shell gas station in Kempner, claiming to have been kidnapped, police said.

"We found out this was a hoax," Sasha Abney's father, Richard Abney, said at a news conference Wednesday evening.

"They missed their curfew, got in deeper and deeper and decided they were going to drive south. They ran out of money and ran out of gas, and they were afraid to call us. We are apologizing to everyone."

He said Ward had even hit her cousin in the head with her shoe to cause a minor injury and lend credibility to their story.

Abney and Ward were picked up by Lampasas police at the gas station Tuesday night after they called in at 9:54 p.m. to report they had "escaped." One of the women claimed they had been kidnapped. A second female was reported to be unconscious in a vehicle parked outside, according to the Lampasas County Sheriff's Department. The women told police they were abducted by force from Mesquite. Ward was "unresponsive but breathing" when approached by deputies, the sheriff's department said.

They were examined for injuries at Scott & White Hospital in Lampasas County and their vehicle was taken by police to search of evidence. The women arrived at the Mesquite Police Department around 4 p.m. Wednesday to tell the story of their alleged abduction. It was that police department that was handling what was then believed to be a criminal case.

"Within just a few minutes, they admitted to the investigators they made the story up," Mesquite police Lt. Bill Artesi told FOXNews.com on Thursday. "You could tell … the dad, well boy, he's mad at them."

He added that the parents were "shocked, they couldn't believe it." That department is closing its case.

Police from four different jurisdictions were involved in the incident, but only one is pressing charges.

The Terrell Police Department received the missing persons reports from the parents; that's the town the women were from. Dallas police investigated reports of a woman hearing someone scream sometime Saturday night and searched the woods in that area. The Lampasas Sheriff's Department recovered the girls at the gas station. Lampasas officials then turned the women over to Mesquite police, since that's the jurisdiction the girls claimed to have been abducted from.

Because Lampasas officials took the story of the alleged abduction from the cousins Tuesday night, that office will handle the charges against them.

Richard Abney said the cousins' behavior was out of character and that they would be punished.

"As a parent you think the worst," he said. "A lot of people out there were trying to help."

The Associated Press contributed to this report.