Castillo, 31, of San Jose, was found dead in the 2200 block of Monroe Street at about 7:25 a.m. Sunday, police Lt. Phil Cooke said.
A passerby called police and reported seeing an unconscious person.
Cooke said investigators are not releasing further details due to the ongoing investigation, but that they are working "diligently" to determine the facts surrounding Castillo's death.
The killing marks the city's first homicide of the year.
Anyone with information about the case is asked to call police Detective Sgt. Kurt Clarke at (408) 615-4828.