In court, Karr, 41, will hear the charges against him and tell a judge whether he will contest extradition, the Boulder County District Attorney's office said Monday.
Karr, who will be provided with a lawyer at the hearing, is being held on a warrant for suspicion of first-degree murder, kidnapping and child sexual assault, though he has not yet been charged with any crime.
"What happens next depends on whether he waives extradition," Oscar Butao, deputy sheriff for the L.A. County Sheriff's Department, tells PEOPLE. "If he does waive it, he'll be in Boulder in a few days, and if he fights it, the case could take weeks to extradite him to Boulder.
Karr's possible extradition to Colorado already has been expedited by California authorities, who have dropped an outstanding arrest warrant against him on 2001 charges of possession of child pornography, reports CNN.
The attorney for JonBenet's father, John, told CNN on Monday that his client's reaction to Karr's arrest was "one of hope" – although he does not know if the case has been solved.
Many questions have arisen about Karr's claims that he was involved in the murder of JonBenet, whose body was found December 26, 1996, in the basement of her family's Boulder home. The evidence against has not yet been revealed.
For now, Karr remains in a small, isolated jail cell in Los Angeles. He is separated from other inmates and being checked by guards every 15 minutes, according to authorities.
The bleak holding cell is a far cry from his trip back from Thailand from which Karr was deported over the weekend. During the flight, Karr flew without handcuffs, with a window seat in business class, sipping champagne and dining on fried prawns and chocolate cake.
Randall Simons / Polaris
Karr was then cuffed and handed over to deputies for transportation via sheriff's helicopter directly from the tarmac to the men's central jail for booking and housing.
Karr arrived at the jail at 11:17 pm and was taken to processing. He is being housed in the central jail's high-powered cellblock, where he is segregated from all other inmates and provided a deputy to escort him within the jail to shower and visitor areas.