Houston ? The capital murder convictions of Andrea Yates were thrown out by an appeals court Thursday, 3 1/2 years after she told investigators that she had methodically drowned her five children in the bathtub to spare them from eternal damnation and to punish herself for being a bad mother.

The court overturned the verdicts because an expert witness for the prosecution told the jury that an episode of the television drama “Law & Order” in which a woman drowned her children in a bathtub aired shortly before the Yates killings. In the purported episode, the mother was acquitted of murder because she was judged insane, according to the witness.

Prosecutors used the testimony to suggest to jurors that Yates was a fan of the show and got the idea from that episode that she could get away with the murders — and, therefore, understood that it was wrong to kill. Jurors took less than four hours to reject Yates’ insanity defense and convict her.

But there was no such episode. The witness, Newport Beach, Calif., forensic psychiatrist Park Dietz, testified that he had served as a consultant for the show, but has since said that he might have confused the story line with one from another television series.

“We conclude that there is a reasonable likelihood that Dr. Dietz’s false testimony could have affected the judgment of the jury,” the judges wrote. “We further conclude that Dr. Dietz’s false testimony affected the substantial rights of appellant.”

The appeals court ruling could mean a new trial for Yates, though prosecutors said they would appeal.

Dietz is a renowned forensic specialist who says he has testified in about 1,000 criminal cases. With rare exception, he has worked as a paid witness for the prosecution, and he has typically carried to the stand a stern message that the mentally ill can distinguish between right and wrong.

Dietz, in an interview Thursday at his home in Newport Beach, said he had made an “honest mistake” in the Yates case and had exhibited no bias.

Yates’ defense lawyers said they were not seeking her immediate release from the psychiatric prison facility in Rusk, Texas, where she is serving a life sentence.