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Police initially thought they were responding to a suicide at the home on the 12900 block of Droxford Street at about 5:30 a.m.
However, when officers arrived at the home, they suspected the death was a homicide. Police said the wife of the victim found the body.
Fighting back tears, Glebovich's daughter told Eyewitness News that her father was shot to death and was a victim of a home-invasion robbery.
There has been a string of home-invasion robberies recently in Cerritos and in neighboring city Bellflower, but nobody has been hurt in those incidents.
Detectives have not confirmed the man was killed in a home invasion, only saying they are investigating a death.
"There is trauma to him, so it is an investigation. We don't know if it's going ot be a criminal investigation, that's how we're treating it for now," said Det. Phillip Guzman from the L.A. County Sheriff's Department.
Guzman said police are waiting for the official cause of death from the coroner's office.
According to neighbors, the victim lived in the Cerritos home for some 39 years, which is how long neighbor Daniel Clark has known him.
"Joe, he was a very giving person," Clark said. "Every time he would go fishing, he would always bring fish back, and give me fish."
The crime scene is right across the street from an elementary school in a community that is known for its safety.
Police have no suspect description and no motive.
Anyone with information is urged to call L.A. County Sheriff's Department at (323) 890-5500.