A child actress whose credits included the film “Jaws IV: The Revenge” was believed to have died with her mother in an apparent murder-suicide initiated by her father, who set fire to the family’s San Fernando Valley home before taking his own life, authorities said. The bodies were found in the heavily damaged West Hills home of Jozsef and Maria Barsi, whose only child, Judith, 11, had also appeared in numerous television shows and about 50 commercials. The coroner’s office said the dead man was Jozsef Barsi, 55. Investigators said Jozsef, a plumber, apparently shot and killed his 48-year-old wife and his daughter in the house, doused their bodies with gasoline and set them on fire before going to the garage and shooting himself in the head with a .32-caliber pistol. The fire destroyed the interior of the house, in the 22100 block of Michale Street. The child’s body was found in her bed and the woman’s in a hallway, Police Lt. Warren Knowles said. Both had been shot once in the head. “It appears a flammable liquid was poured on the child, or on the child’s bed,” Knowles said. “It looks to me as if the male found in the garage caused the death of the other adult and child and then apparently killed himself.” Police said the pistol was found in the father’s hand and a gas can lay about 4 feet from his body. On an episode of “Murder House Flip,” the current owners revealed that the garage door would open and close on its own, and they’d feel cold spots throughout the house. Gaby Bernal, who slept in the same bedroom where Judith was murdered, also suffered from terrible nightmares.