More than 20 ex-judges and prosecutors asked Governor Rick Perry to stop the scheduled execution of Charles Dean Hood.
They want the September 10th execution delayed until a hearing on whether a now-former judge and a prosecutor had an unethical romance during the trial.
Perry's office had no immediate response.
Hood was condemned for the 1989 fatal shootings of Tracie Lynn Wallace and her boyfriend in Plano.
Hood's lawyers contend the alleged secret relationship between now retired Judge Verla Sue Holland and ex-Collin County District Attorney Tom O'Connell tainted the trial.
Holland and O'Connell have declined to address the allegations.