Baird presided over an October hearing into whether Cameron Willingham was wrongly executed for setting a 1991 fire that killed his three daughters. Many fire experts now say the blaze was accidental.
Attorneys from the Innocence Project are trying to clear Willingham's name and get the state to acknowledge he was wrongly executed.
A Texas prosecutor sought Baird's recusal, questioning his impartiality. Baird declined to rule on the motion, saying the prosecutor didn't have standing in the case.