(CNN) -- A Texas judge rebuffed a request to step aside Thursday and opened a hearing into allegations that a man executed for the killings of his three daughters was put on death row by "junk science."
The family of Cameron Todd Willingham has asked District Judge Charlie Baird to posthumously clear Willingham's name, arguing that state officials ignored an expert's last-minute findings that the fire that killed his daughters in December 1991 was not deliberately set. The science that supported the prosecution's case "had been discredited 10 years earlier," Gerry Goldstein, a lawyer for the family, told the judge.
Willingham was put to death in February 2004, insisting in his final statement that he was innocent. Authorities in the town of Corsicana, where the fire took place, and Texas Gov. Rick Perry, who allowed the execution to go forward, have stood by the conviction.
Navarro County District Attorney Lowell Thompson last week asked Baird to step aside. Thompson argued that the judge's impartiality was called into question by the fact that he sat on the state Court of Criminal Appeals when it upheld Willingham's conviction and wrote a concurring opinion supporting the ruling. In addition, he argued, Baird received an award in February from the Texas Coalition to Abolish the Death Penalty.
Baird rejected Thompson's motion Thursday, finding that the prosecutor's office was not a party to the family's request for a "court of inquiry," a rare proceeding under Texas law.
"I just don't believe that you, in your capacity as the Navarro County district attorney, are a part of this lawsuit," Baird said.
Thompson left the courtroom after the ruling without participating in Thursday's hearing, which was held to determine whether there is enough evidence of a wrongful conviction to open a court of inquiry. The proceedings are separate from the long-running investigation being conducted by the Texas Forensic Science Commission, which is scheduled to take up the Willingham case again Friday.
Willingham's relatives have the support of The Innocence Project, which requested the Forensic Science Commission's investigation. The group's founder, defense lawyer Barry Scheck, appeared in court Thursday to argue for a court of inquiry, telling Baird the testimony of a state fire marshal who was the prosecution's key witness was "completely wrong and misleading."
The fire marshal, Manuel Vasquez, told jurors in Willingham's trial that evidence at the scene of the fire showed the blaze was set intentionally with a flammable liquid.
"Given the science that we know today," Scheck said, that testimony is "false, misleading and totally unreliable."
Fire scientist John Lentini, who reviewed the Willingham case after the execution, told Baird that some of the indicators Vasquez relied on to reach his conclusions were outdated at the time -- and nearly all were considered obsolete by the time Willingham was executed.
"A lot of people believed that back in 1991," Lentini said. "Now in 2004, nobody believed that."
Vasquez died in the mid-1990s, but the state fire marshal's office has reaffirmed his findings -- a stance Lentini said was impossible to square with modern fire science.
"You can't make it go away just by saying, 'We stand by the original conclusions,' " he said.
Willingham's daughters -- 2-year-old Amber and 1-year-old twins Karmon and Kameron -- died in the blaze in Corsicana, south of Dallas. His ex-wife, Stacy Kuykendall, told reporters outside the Austin courthouse last week that Willingham had confessed to her in the days before his execution that he had started the fatal fire.
"He burnt them," Kuykendall said. "He admitted he burnt them to me, and he was convicted for his crime. That is the closest to justice that my daughters will ever get."
Willingham never publicly admitted guilt, and his family has questioned Kuykendall's account of the confession. Baird said Kuykendall was invited to appear at Thursday's hearing, but she declined.