(CNN) -- Jesse Matthew, a suspect in the disappearance of University of Virginia student Hannah Graham, was questioned in connection with an alleged sexual assault nearly 12 years ago, authorities said Thursday.
However, no charges were filed because the woman didn't want to go forward with the case and investigators determined there wasn't enough evidence to arrest Matthew, said Michael Doucette, the Commonwealth's Attorney for Lynchburg, Virginia.
According to a statement from Lynchburg police, a woman reported she was raped on the campus of Liberty University on October 17, 2002.
Matthew told authorities that the woman consented, Doucette said, adding that there were no witnesses.
On Thursday, Matthew was sitting in a Texas jail cell, waiting for Virginia authorities to pick him up and take him back to Charlottesville, where he has been sought in the Graham case on suspicion of abduction with the intent to defile.
He was in a Texas court twice Thursday. The second time, Judge Michelle Slaughter in Galveston asked whether he wanted to fight extradition or would agree to be sent to back to Virginia.
Matthew agreed to the extradition.
Charlottesville Police Chief Timothy Longo told reporters that he thought Matthew would be moved Friday. He had no comment when asked about the 2002 case.
Earlier, Matthew appeared before Galveston County Judge Mark Henry on a charge of giving false information to a Texas peace officer.
Authorities found Matthew on a Galveston County beach some 1,300 miles from where he's wanted in the disappearance.
Deputies were tipped off to Matthew's whereabouts when they got a call about a suspicious person camping on the beach. One responded and ran the license plate of that person's vehicle. It came back as wanted, CNN affiliate KPRC reported.
Matthew did not resist arrest, Galveston County Sheriff Henry Trochesset told reporters Thursday. The sheriff added that investigators from Virginia were examining a car and a tent found at Matthew's campsite and hoped to speak to Matthew later.
Matthew's Virginia-based lawyer had little to say about his client when approached earlier outside his Charlottesville office.
"I am Mr. Matthew's attorney," James Camblos said. "I was hired on Saturday. That's the only thing that I'm going to confirm at this point. The family and I -- nobody is making any statements at this point in time. We might later on, but right now we are not."
His comments came a day after authorities obtained an arrest warrant for his client, who police believe was the last person with Graham.
Matthew willingly went to a police station over the weekend, when there was no warrant for his arrest, Longo said. He asked for a lawyer. They spoke and then left, the police chief said.
Authorities are now offering a $100,000 reward for information leading to the safe return of Graham, 18, a second-year student at the University of Virginia.
The Northern Virginia native is 5 feet 11 inches tall with a slender build and has light brown hair, blue eyes and freckles. She was last seen September 13 wearing a black crop top and capri pants. She had an iPhone in a pink case.
"We have no idea whatsoever where she is," Longo said Thursday.
They have received 1,500 tips so far in the case and are urging anyone with information to call the police tip line at 434-295-3851.
Graham was last seen in an area of Charlottesville known as the Downtown Mall. Investigators have been looking for her since, and over an increasingly large area.
"We're asking for a broader community search with property owners," Longo told CNN's "Anderson Cooper 360" on Wednesday night.
Specifically, he said he wants owners of large parcels of property in surrounding counties to search their land and report back.
Authorities have previously searched Matthew's apartment and car. Although they have declined to discuss the specifics of what might have been found, potential evidence was sent to a lab for analysis.