I posted previously about the conviction and execution of Cameron Todd Willingham in Texas. Now that Perry is running for President, you should expect the case to return to the news.
In summary, Willingham was convicted for the murder of his three children. Although the evidence at the trial was shaky and inappropriate (such as experts testifying that Willingham's skull and crossbones tattoo fit the profile of a sociopath), the jury convicted Willingham and he was sentenced to death. Perry's children died in a fire that the State of Texas said Willingham deliberately set.
A subsequent investigation by the Texas Forensic Science Commission revealed that the forensic report of arson used at the trial was wrong and that the evidence did not support arson. The prosecutor admitted that the original report was flawed but maintained that other evidence (the sociopathic tattoo, I suppose) supported the conviction.
After learning of the new report Governor Perry refused to stop the execution.
Here's the part that reflects really poorly on Perry: After Willingham was executed, the Texas Forensic Science Commission planned to take testimony regarding the original and subsequent arson investigations to try to determine whether there was any possibility that the fire was caused by arson. Because the Texas Forensic Science Commission was a state government agency, Perry had appointment power. Shortly before the hearing, he fired three members of the commission, including the chairman, and replaced them with people who opposed holding the hearing. The commission did not have enough votes to proceed with the hearing, thus burying the truth. What could possibly be wrong with finding the truth?
Wikipedia has a good article:
http://en.wikipedia.org/wiki/Cameron_Todd_Willingham