The panel heard arguments on the appeal March 3 and will issue a written ruling at its headquarters in San Francisco at 10 a.m. Monday.
Davis, 54, was convicted in Santa Clara County Superior Court in 1996 of 10 counts, including first-degree murder and kidnapping, and was sentenced to death.
The trial was moved from Sonoma County to Santa Clara County because of extensive publicity about the case.
Klaas was kidnapped from a slumber party at her mother's home in Petaluma on Oct. 1, 1993.
Her body was found two months later near U.S. Highway 101 in the Cloverdale area after Davis, who had been arrested for a parole violation, led investigators to the location.
Davis's appeal to the state high court is the first step in the lengthy death penalty appeals process in California. If the court upholds his conviction and penalty, David can pursue further challenges through habeas corpus petitions in state and federal courts.
Davis raised about two dozen arguments in his appeal, but the main issue argued before the court in March was his claim that two jailhouse confessions he made after being arrested should not have been allowed as evidence.
He claims the use of the confessions violated his right to have a lawyer.
Prosecutors contend that officers' initial questioning of Davis was justified by a concept known as the rescue doctrine, in which police can question a suspect with no attorney present if they have hope of rescuing a kidnap victim.
Davis later waived his right to have a lawyer and told investigators he strangled Klaas on the night he kidnapped her.
Davis had a long criminal record, with previous convictions for burglaries, assault and two kidnappings of women. His case led to California voters' enactment in 1994 of the state's "three strikes" law, which provides lengthy sentences for repeat offenders.