(CNN) -- The head of a Texas agency investigating whether a faulty arson probe led to a man's 2004 execution said Tuesday he's not a "political pawn," but would not say when the controversial investigation will move forward.
John Bradley was named chairman of the Texas Forensic Science Commission days before the agency was to hear from an expert who criticized the case against Cameron Todd Willingham, who was put to death in 2004 for setting a fire that killed his three daughters.
Texas Gov. Rick Perry allowed Willingham's execution to go forward, and his replacement of the previous chairman and three other members of the forensic panel has led to accusations that he is trying to short-circuit the probe as he faces re-election in 2010.
Bradley told a state Senate committee that neither Perry nor any of his aides gave him any instructions about how to do his job, and said he would have considered that "inappropriate" if it had happened.
"I don't see myself as being someone else's political pawn, and I don't think you've seen that I ever behaved that way," Bradley told a state Senate committee Tuesday.
The Forensic Science Commission launched an investigation of the Willingham case in 2008 after two reports by outside experts concluded that arson investigators mistakenly concluded Willingham had set the fatal fire in 1991. The expert hired by the commission, Craig Beyler, concluded in August that the arson finding "could not be sustained" either by current standards or those in place at the time.
Perry has said he remains confident of Willingham's guilt, calling him a "monster." And authorities in Corsicana, who brought the case against Willingham, say other evidence beyond the forensic testimony in his 1992 trial support the prosecution.
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Bradley -- a district attorney known as a hard-liner in capital cases -- said the commission may have overstepped its authority and needs new rules before the probe can continue. And he warned that the commission should be not be "hijacked" by people using it "as a forum for their personal missions."
The nine-member panel "is not charged with debating the death penalty, not charged with deciding whether people are guilty. And the work of the Commission on Forensic Science will take as long as it deliberately takes," he said.
Bradley said the Willingham investigation "absolutely" will continue. But he would not say when it will hear from Beyler.
"If I had a set of rules I could tell you what the timetable for commission would be," he said.
Willingham maintained his innocence in the final statement he gave before his execution in February 2004.
His cousin, Patricia Cox, said the family was "disappointed" by Bradley's testimony and fears his call for new rules will cause a delay that could undermine the commission's investigation.
"This was an investigation that had gotten to its mid-level," Cox said in a phone interview from her home in Ardmore, Oklahoma. "It had already certainly advanced far too far, I think, to interrupt it."
One of the commission's former members told CNN in October that the Forensic Science Commission had reached a "crucial point" in the Willingham investigation when Perry replaced the four commissioners, whose terms had expired. Cox said the shakeup has "sabotaged the commission and its effectiveness."