(CBS/AP) SAN FRANCISCO - Convicted murderer Scott Peterson filed an automatic appeal to the California Supreme Court on Thursday, eight years after he was sentenced to death for the murders of his wife and unborn son. 

In the appeal, his lawyer argued that the overwhelming publicity the trial received, incorrect evidentiary rulings, juror misconduct and other errors deprived Peterson of a fair trial.

A San Mateo County jury found the former fertilizer salesman guilty of suffocating Laci Peterson and dumping her in the San Francisco Bay on Christmas Eve 2002.

Peterson was convicted in 2004, although he maintained his innocence throughout the trial. He claimed that Laci was killed sometime in the morning of Dec. 24, 2002 after he left their Modesto home to go fishing in the San Francisco Bay. Death penalty lawyer Cliff Gardner noted that Peterson was convicted and sentenced to death even though investigators never directly proving "how, where or when" the murder occurred, The Associated Press reported.

Prosecutors told the jury that Laci was killed sometime between the night of Dec. 23, 2002 and the morning of Dec. 24, 2002. They believed Laci was suffocated in her home, but Gardner argued that there was little direct evidence collected at the house to support that theory.

Gardner argued that case generated intense publicity almost from the moment Laci disappeared, depriving Peterson of a fair trial.

"Before hearing even a single witness, nearly half of all prospective jurors admitted they had already decided Mr. Peterson was guilty of capital murder," Gardner claimed.

Read more at cbsnews.com

Guest: Michael Cordoza who cross examined Peterson joins at 12:35