Assemblyman Mike Gatto told the Los Angeles Times his sister found their father's body Wednesday evening. He said she went to the house because she had been unable to reach Joseph Gatto all day.
Investigators said Gatto, 78, had been shot at least once in the chest and the weapon was believed to be a small caliber handgun. Someone had gone through the house, apparently searching for valuables, but police were unsure if anything had been taken.
Gatto's body had fallen across a desk, police said.
The homicide was the first this year in the city's Silver Lake neighborhood, a trendy area that is generally considered safe.
Mike Gatto, a Democrat, was elected to the Assembly in 2010 in a special election and won a full term in November that year.