(CNN) -- DNA testing shows that a slain British student had sex with one of the suspects being held in the case, the prosecutor's office said Thursday.
Rudy Hermann Guede was arrested in the German city of Mainz.
A vaginal swab taken from the body of Meredith Kercher was matched to DNA from Rudy Hermann Guede, the office said. Guede, 20, was arrested in the case this week in Germany.
Police say Kercher, an exchange student at Perugia's university, was killed late on November 1 in the villa where she lived. She was found the next day, half-naked, with a stab wound to her neck.
It was unclear whether sex between Kercher and Guede was consensual. A report issued by an Italian judge last week suggested the young woman may have been sexually assaulted at knifepoint before she was killed in her bed.
Guede maintains his innocence, but has said he will not fight extradition from Germany, a spokesman for the German prosecutor said Thursday.
Italian police have connected Guede to a bloody fingerprint on a pillow at the crime scene, and DNA tests have linked him to the villa through skin cells found on toilet paper there.
In the arrest warrant from an Italian judge for Guede, the judge says fears that the man may kill again are another reason he needs to be in custody, according to the prosecutor's office in Perugia.
Earlier, the prosecutor's office said no DNA from Kercher was found on the shoes of another suspect in the case, Raffaele Sollecito.
Sollecito's shoe appeared to match a print found on a duvet under which Kercher's body was found, the prosecutor's office said.
Sollecito is the boyfriend of Kercher's American roommate, Amanda Knox, 20, who is also being held in the case.
Knox has told police she's not sure what happened the night her roommate was killed in the Italian villa they shared -- but that she did not kill Kercher.
Knox, who is still in custody, wrote a four-page statement for police the day she was questioned about Kercher's death, saying she was confused about the events of that night, but wanted "to tell the truth as best I can."
Knox wrote in her statement, a copy of which has been obtained by CNN, that she's not sure whether she was at the villa that night and that she remembers "flashes of blurred images," but doesn't know if they are reality or dreams. Knox said she believes she spent the night at Sollecito's home.
Meanwhile, Sollecito's lawyer, Luca Maori, said investigators issued their findings from an examination of his client's computer, which Sollecito said he was using at home when Kercher was killed.
Maori said the Italian Postal Police concluded the computer was turned on that night but was not necessarily being used. Maori contested their findings, saying the police's instruments weren't sophisticated enough to make a proper finding.
Wednesday, Maori said the defense team had examined a clone of Sollecito's hard drive that showed he was in his house and using the computer from 8:30 p.m. on November 1 to 1:33 a.m. on November 2. Police have said Kercher died between 10 p.m. and midnight on November 1. E-mail to a friend
CNN's Diana Magnay and Hada Messia contributed to this report.