AUSTIN — The Texas Board of Pardons and Paroles has denied a petition by a New York-based nonprofit group for a posthumous pardon of a man executed for killing his three children in a house fire.A letter from the parole board released last week said the agency has denied a pardon for Cameron Todd Willingham, whose case has been cited by wrongful-conviction advocates who argue Texas’ death-penalty system is severely flawed. Willingham was put to death in 2004 for the deaths of his three daughters in a house fire in Corsicana. A state fire marshal who studied the scene testified at Willingham’s 1992 trial that the fire was arson. Scientists have since refuted much of the methodology used by arson investigators before 1992, including the techniques used by the fire marshal in the Willingham fire. Attorneys submitted new scientific findings to Gov. Rick Perry in 2004 and asked for time to reopen the case, but Perry allowed Willingham’s execution to go forward that year. Willingham maintained his innocence until his death. The Innocence Project, which has continued to argue Willingham’s case after his death, has also argued the prosecutor at his trial quietly helped get a jailhouse informant a lighter sentence in exchange for testimony that Willingham confessed. The prosecutor, John Jackson, denies the allegation. The Innocence Project said in a statement Thursday that the parole board’s decision “illustrates that the clemency system is completely broken in Texas.” “The Board’s indifference to the question of Willingham’s innocence as well as the integrity of the information it relies on in making its decision highlights the dire need for reform,” project co-director Barry Scheck said in a statement. The group will not be able to apply again to the parole board on Willingham’s behalf for two years. Texas has granted posthumous clemency only once, to Tim Cole, who died in prison after being convicted of raping a Texas Tech University student. DNA evidence tied another man to the crime and exonerated Cole after his death. The state later passed an act named after Cole that provides exonerated inmates with $80,000 for each year of wrongful imprisonment and other compensation.