Good morning, Mr. Peterson. Can you both see and hear the proceedings, sir? Yes, sir. Thank you. Convicted murderer, Scott Peterson, appearing virtually in court today for the first time since his case was taken on by the Los Angeles Innocence Project.

We spent a lot of time trying to suss out what, frankly, are very alarming deficiencies in the discovery that was provided to the defense at the time of trial.

The 51-year-old zooming in from Mule Creek State Prison with a striking new look. His hair pulled back into a ponytail. Trial, listening in as his new legal team made their first public arguments after filing a bombshell motion.

Mr. Peterson has been waiting 20 years to find some of these police reports and audio recordings and video recordings that should have been provided.

Peterson's lawyer is insisting he did not kill his eight and a half month pregnant wife, Lacy, and their unborn child, and says new and overlooked evidence could exonerate him. The original prosecutors who tried the case in 2004 were back in the courtroom today.

A lot of these issues have been raised and have been adjudicated.

The Innocence Project calling for them to be removed, arguing in part, they are heavily invested in upholding a conviction they played a major role in obtaining. The judge allowing proceedings to move forward for now, scheduling three new hearings, including one in May, that will determine whether DNA from a bloody mattress found in a burned-out van will be retested.

There's no doubt that any The hearings being scheduled in connection with this case are a small victory for Scott Peterson. In most cases, when someone makes a motion 20 years later to reevaluate the evidence, it's rejected. Here, the judge is at the least taking very seriously the questions involved.

John Buhler was a lead investigator on the case.

Well, I'm A-OK with them not dismissing it out of hand. If you come up with evidence, either before trial, during trial, or after trial, test it, shake it out, see what it's all about. I have no doubt that Scott did it.

Peterson's family smiling as they walked out of the courtroom, Lacy's family refusing to attend.

In In perfect world for Scott Peterson, he would get a new trial. But trying someone 20 something years later, it gets a lot harder. Memories have fated. Witnesses will have died. It fundamentally changes a trial.

Peterson But in the Peterson's Innocence Project attorneys claim that from the start, authorities zeroed in on the wrong man, claiming there were witnesses who say they saw Lacy on the day she went missing, who were not properly interviewed.

There are a number of other witnesses who we have been investigating.

They also claim a burglary across the street from the Peterson home happened on the same day Lacy went missing and was not fully investigated.

Their allegation here is that some witnesses believed that Lacy Peterson interrupted that burglary, and then she was killed because of it by those who were involved in it.

The Innocence Project also asking for more extensive DNA testing of a piece of fabric found in a burned-out van, a a while away the day after Lacy's disappearance.

That orange van had actually been seen where one of the witnesses saw Lacy. So there was a connection between the van and a possible Lacy siding.

So somebody's blood is on a mattress in the back of a a van that was burned deliberately. Who?

That a burned van was found not far away from their home by the Modesto Airport? You got to admit, even if police were able to clear those, coincidentally, that's weird.

Former Modesto fire inspector, Brian Spetolsky, responded to that burned-out van on Christmas morning, the day after Lacy went missing.

There was a stain back there that presented as a rust-colored stain.

Spitalski says that he and the Modesto Police Department tested the mattress, and it came up positive for human blood.

I don't know that I was tying the moment to Lacy. I was more tying the moment that it was human blood. It made it like this was much more important than just a burned vehicle that somebody was just wanting to get rid of or cover up. We cut off a piece of the fabric. It went into an evidence container, an envelope, and that was taken to the Department of Justice.

The Innocence Project also says the full results from the police investigation were never shared with Peterson's defense team at trial. His original lawyer, Mark Garagos. Motion claims that there was blood found in the van, and it was likely never tested again. Lacy's DNA, was your teammate aware of this?

Not in real-time, no. And by the way, we were getting dumped discovery, literally while we were trying the case. I was never contacted. I don't want to point fingers at anybody, but it definitely was an important piece of evidence evidence that needs to be addressed.

The mattress samples were tested in 2019 at the request of Peterson's defense team, but results were inconclusive, and the Innocence Project wants them tested again.

The Innocence Project, who are experts on DNA, thinks that better samples can be taken, and there are different procedures and newer scientific methods that may be able to sequence that DNA to determine whether it's associated with a crime. If Lacy's DNA is in that van, then the case is over.

The judge today is scheduling a date in May to decide whether or not they will retest those samples for DNA.

If that happens, that's a big win for Scott Peterson.

I have no doubt that Scott did it, and I have no doubt that if they do repetitive testing on the blood that was found in that mattress from the burned-out van, that it's not going to reveal anything that has anything whatsoever to do with the Peterson case.

Peterson has repeatedly appealed for a new trial, so far with no success. But his death sentence was overturned to life in prison after the California Supreme Court ruled that his jury was improperly screened for bias against the death penalty. Peterson has always maintained he did not kill his wife.

This is a brutal thing for Lacy's family and her friends to have to go through every couple of years when they come up with some new idea. It just dredges up these feelings of tragedy of us.

In a statement after today's hearing, the Los Angeles Innocence Project stated that it was just the first step in a long process, and that they will continue to present our case in court where it should be adjudicated.

When Scott Peterson's death penalty was over termed, it was a big deal, but it seemed that was the end of the road. The fact that the judge is at least taking this seriously offers a glimmer of hope to the family of Scott Peterson.

Our thanks to Cana. You can watch more of Impact by Nightline, Scott Peterson, the wrong man, now streaming on Hulu.

Hi, everyone.

George Stefanopoulos here. Thanks for checking out the ABC News YouTube channel. If you'd like to get more videos, show highlights, and watch live event coverage, click on the right over here to subscribe to our channel. And don't forget to download the ABC News app for breaking news alerts. Thanks for watching.