Relatives of Cameron Todd Willingham, attorneys from the Innocence Project, the Texas Defender Service and other law firms contend his conviction was based on faulty investigative techniques, The Texas Tribune reported.
"My son Todd was convicted on false evidence," Willingham's stepmother, Eugenia Willingham of Ardmore, Okla., said outside the Texas Capitol in Austin. "How I'd like to be proud of the Willingham name again.
"We felt so helpless not having the resources to help him. I can still remember the hurt, the anger he felt."
It wasn't clear when the state Board of Pardons would address the family's application, but board spokesman Harold Battson said such cases usually take 3-4 months to review, the Tribune said.
Texas has never officially recognized that it has put an innocent person to death, the online news outlet said.
Willingham was executed eight years ago for the 1991 deaths of his children in the blaze at his Corsicana home.
Two fire investigators determined the burn damage indicated arson, but another fire expert later suggested the forensic methods used to arrive at that conclusion were deeply flawed, the Tribune said.
Willingham's former wife, Stacy Kuykendall, believes he was guilty of killing their children. "My ex-husband murdered my daughters," she told reporters in 2010. "And just before he was executed, he told me he did it."
Willingham's trial attorney has also said he believed his client was guilty.
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