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Davis' lawyer argued that police violated the law by not telling his client what his rights were when they got a confession out of him.
"The police initiate contact with him under the guise, if you will, of getting more prints although they've got his palm print matched to the bedroom already," Phillip Cherny said.
Deputy Attorney General Ronald Mathias told the court, the law gives police the right to interrogate a suspect without reading him his rights if they believe the victim is still alive.
"There was absolutely nothing known to police on December 4 that would have compelled them to assume Polly was dead," he said.
12-year-old Polly Klaas was kidnapped from her bedroom from a slumber party at her mother's home in Petaluma in October of 1993.
Polly's disappearance led to a massive well organized search effort. Her body was found two months later at an abandoned lumber mill in Cloverdale.
Davis led police to her body after being arrested on a parole violation. He confessed to police, saying he strangled the girl soon after kidnapping her.
Davis' trial was moved from Sonoma County to Santa Clara County because of the extensive publicity surrounding the case.
The twice convicted felon was convicted and sentenced to die in 1996.
Polly's father Marc Klaas told ABC7 afterwards, he believed the justices agreed with the government's arguments.
"The reasonable expectation that my daughter could still be alive was more important than his immediate right to representation," Klaas said.
The justices now have three months to issue a written ruling. If they decide to uphold the conviction, Davis' lawyer can appeal to federal courts and challenge the constitutionality of his conviction.
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