▶ Watch Video: Sneak peek: Scott Peterson: Case in Question It was one of the most sensational crime stories of the last 20 years. The case attracted national and international media attention. There are parallels between Scott Peterson, the handsome, eerily unemotional husband whose wife goes missing and the Ben Affleck character in the blockbuster movie “Gone Girl.” Scott Peterson was sentenced to death for the murder of his pregnant wife Laci and their unborn child in 2005. But after appeals, his death sentence was overturned. His defense team told CBS News correspondent Jonathan Vigliotti they also have new exonerating evidence and are pushing for a completely new trial. Vigliotti reports on the case for “48 Hours” in “Scott Peterson: Case in Question” airing on Saturday, May 1 at 10/9c on CBS. Scott and Laci Peterson Court evidence To those who knew them, Peterson and his pregnant wife Laci looked like the all-American couple — good-looking, social, and starting a new family — until, on Christmas Eve 2002, Laci vanished. Scott Peterson’s alibi for the day Laci disappeared was unusual. He said he made a solo Christmas Eve fishing trip to chilly San Francisco Bay, 90 miles from his home in the Central Valley city of Modesto. He later made what detectives called a suspicious sounding call to Laci’s answering machine the day she disappeared. Months later, the bodies of Laci and their unborn child, whom they had named Connor, washed up in San Francisco Bay very close to the area where he had been fishing. And then it turned out that Peterson had lied to police about the state of his marriage. He had told them it was fine. But there was another woman in Scott’s life — he’d been having an affair. Amber Frey was a young, attractive massage therapist. Peterson convinced her that he was single and looking for love. Frey’s stories of Scott’s endless lies and deceptions helped turn America’s impression of him from charming everyman into a playboy sociopath. And finally, on the day of his arrest, cops say Peterson led them on a high-speed freeway evasion. When they caught up with him, he had dyed his hair blond and had $15,000 in cash and camping gear in his car. After a six-month trial that captivated the public and made stars of several media commentators, Scott Peterson was convicted and sentenced to death. Scott Peterson AP But last summer, the California Supreme Court threw out Peterson’s death sentence. The court decided that the original judge in the case had made an error during jury selection. The result of that mistake, Peterson’s supporters say, was that the jury was stacked against him with pro-death-penalty jurors. A new trial has been ordered on the death penalty phase of Peterson’s case. In addition, there is a separate court battle over one of the jurors in the original case. Peterson’s defense team says she lied about her background on a questionnaire before she was selected for the jury. Prosecutors insist she didn’t lie — she simply didn’t think her past experiences were relevant to the questions. Later this year, a lower court judge is expected to decide whether Peterson will get a new trial on his guilt or innocence. The case remains fascinating for several reasons. It was a circumstantial evidence homicide case; there was little hard, forensic evidence. Now, the internet has sparked a noisy community of “amateur sleuths,” including some of Peterson’s family members, and assorted true-crime enthusiasts who believe Scott is innocent. Though Scott Peterson’s defense team won’t reveal exactly what new evidence they say they’ve discovered, they claim to have new witnesses who saw Laci Peterson alive after the time authorities say she was murdered. They also claim to have suspects who they believe were Laci’s real kidnappers and killers. But one of the original detectives on the case, Jon Buehler, told “48 Hours” there is nothing that has emerged that would make him change his view that Peterson got a fair trial and is the one who killed Laci. “Well I guess it’s possible,” says Buehler. “But you know, there’s still people that believe the earth is flat, too.” Peterson’s next court date will be in June.