Kohberger's father is expected to testify before the impaneled grand jury in a sealed proceeding in Pennsylvania Thursday, according to the source.
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His mother previously testified before the secretive panel, the source said.
The parents of the man indicted for the killings of four University of Idaho students were subpoenaed in the Pennsylvania jurisdiction where they live and where Bryan Kohberger was arrested last December.
Their compelled testimony under oath may be shared with prosecutors in Idaho, according to the source. Pennsylvania law allows judges to release transcripts of witness testimony before grand juries to other investigative agencies after a court hearing.
An attorney representing Kohberger's parents tried unsuccessfully to have the subpoenas quashed, the source said.
The attorney retained by Michael and Maryann Kohberger declined to comment to CNN about the grand jury proceedings.
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The Latah County Prosecutor's Office declined to comment to CNN citing the gag order in effect in the Kohberger case.
By law, a Monroe County grand jury can only review potential crimes that occurred within Monroe County, Pennsylvania. It is unclear what potential crime they are investigating.
On Thursday, the Stroud Area Regional Police Department said it is aware of some media outlets reporting connections between Kohberger and the investigation into the disappearance of Dana Smithers, a woman whose remains were found in Stroudsburg, Pennsylvania last month.
Police said there's no evidence to support those claims.
"The SARPD has no evidence that Dana Smither's disappearance, is in any way tied to Idaho murder suspect Bryan Kohberger," said Jennifer Lyon, chief of police.
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Grand jury proceedings are secretive by nature and documents related to the proceedings are sealed.
Kohberger was arrested at his parents' Pennsylvania home, almost seven weeks after Kaylee Goncalves, 21; Madison Mogen, 21; Xana Kernodle, 20; and Ethan Chapin, 20, were found dead November 13 in an off-campus home in Moscow, Idaho.
He drove from Pullman, Washington, where he was studying criminal justice to Pennsylvania for the holidays with his father and stayed at the family home from mid-December until his arrest in the early hours of December 30, CNN has previously reported.
After his arrest law enforcement searched the home and Kohberger's white Hyundai Elantra, which authorities had been looking for in connection with the killings.
Kohberger was extradited to Idaho to face the murder charges in January.