The body of Kohberger's 3-month-old son, Alijah Mullis, was found last month along a remote Texas road, not far from his car seat.
The boy's father, 21-year-old Travis Mullis, has been charged with capital murder after he allegedly told police he stomped the boy's head in order to make the infant stop crying.
Authorities are accusing Kohberger of allowing Mullis to take the baby from the family's house in Alvin in the early morning of Jan. 29, even though he had made menacing statements toward the child.
Kohberger has not waived extradition to Texas, and Brazoria County District Attorney Jeri Yenne said her office will begin the process next week to bring her back.
If convicted, Kohberger faces up to two years in state jail. Meanwhile, Mullis provided authorities Friday with a DNA sample after a request by prosecutors that he give a sample so investigators could compare it to evidence collected when the baby's body was found.
Galveston County District Attorney Kurt Sistrunk said he has not decided whether to seek the death penalty against Mullis.
Mullis' attorney, Robert Loper, said his client gave the DNA willingly. The attorney said prosecutors will probably seek an indictment next week against Mullis.
Alijah's body was found Jan. 29 by a couple driving along a road looking for wildlife. The body had been tossed out onto the side of a road while still inside a child safety seat, then apparently fell out of the seat when it hit the ground.
After a nationwide manhunt for Mullis, he turned himself in to Philadelphia police. He waived extradition and was brought back to Galveston, where he remains jailed under a $1 million bond.
