( 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 did n'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 .
Frank Martinez Garcia was convicted of murdering his wife and a police officer . He also wounded a relative and fired at a nearby elementary school . The U.S. Supreme Court turned down his last-minute appeal Thursday .