Crespo, 45, was shot on Tuesday at his home during an argument with his wife, Levette, 43, and his 19-year-old son, the Los Angeles Times reported.
An altercation between Crespo and his wife began in the master bedroom, during which his son, Daniel, intervened, police officials said.
While father and son were fighting, Crespo's wife got a gun and shot Crespo.
Crespo died on way to a hospital, the officials added.
Crespo's wife was taken into custody while his son was taken to a hospital to be treated for injuries sustained on his face from the struggle and was later questioned by authorities.
Hailing from Brooklyn, Crespo was a teenager when he married Levette, his high school sweetheart, in 1986.
Crespo was first elected to the city council in 2001 and worked as a Los Angeles county probation officer for more than a decade, a job he continued to hold after becoming mayor of Bell Gardens last year.