HUNTSVILLE, Texas — Attorneys for a Texas prisoner facing execution this week for killing a woman in Dallas in 1999 are asking the U.S. Supreme Court to halt his punishment after the top Texas criminal court refused to consider their appeal.

Lawyers for 64-year-old William Rayford say his execution set for Tuesday evening in Huntsville should be halted so the high court can review whether his trial lawyer during questioning of a witness improperly introduced race as a possible factor jurors could have considered when they decided Rayford, who is black, should die for killing his ex-girlfriend Carol Lynn Thomas Hall.

The Texas Court of Criminal Appeals said Friday Rayford’s appeal was improper for procedural reasons and rejected it. Two of the court’s nine judges say they would have stopped the execution.