(CNN) -- A Texas man convicted of murdering a San Antonio police officer before turning his gun on his wife was put to death Thursday evening, soon after the U.S. Supreme Court rejected his last-minute appeal.





The time of death for Frank Martinez Garcia was 7:02 p.m. CT (8:02 p.m. ET), said Texas Department of Criminal Justice spokeswoman Becky Blanton.





Garcia was 28 on March 29, 2001, when San Antonio police officer Hector Garza responded to a call about a domestic disturbance at the home Garcia shared with his parents, his wife, Jessica, and their children.





Garza, 49, died first after being shot three times by Garcia, the Texas Department of Criminal Justice said on its website. Garcia's wife died after he shot her six times.





He also fired several shots at others outside the home, wounding his wife's uncle, according to authorities. The couple's 5-year-old daughter witnessed the murders, according to the Department of Criminal Justice.





The office of Texas Attorney General Greg Abbott stated, on its website, that Garcia -- who had been arrested with gang members in 1992 -- also fired his weapon at the vice principal of a nearby elementary school, hitting the front door of the school.





Garcia eventually surrendered to police, later admitting in a formal written statement that he had intentionally killed both the police officer and his wife, according to the attorney general.





A Bexar County grand jury indicted him in September 2001 for capital murder.





During his trial, jurors saw photos from inside Garcia's home showing him and his wife brandishing weapons. Prosecutors also noted that his wife Jessica sought help from a battered women's shelter in 1994, after alleging physical and emotional abuse, while her co-workers had seen marks and bruises on her.





In February 2002, Garcia was convicted and sentenced to death.





The Texas Court of Criminal Appeals affirmed his conviction two years later. And in 2007, the same court denied his application for habeas corpus relief -- in other words, claiming the state didn't have a right to hold him -- according to the attorney general.





A U.S. district court turned down a similar petition in 2009, and a U.S. Circuit of Appeals court rejected his appeal the following year. In March 2011, the U.S. Supreme Court denied his writ of certiorari review, a legal term related to a higher court reviewing a lower court's decision.





CNN's Bill Mears and Nick Valencia contributed to this report.
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