Reports are that investigators found heroin in the apartment.
The actor himself had admitted to the TMZ Web site that - whereas he had been drug-free for 23 years - a year ago he had fallen off the wagon and begun taking pills and sniffing heroin.
Scriptwriter David Katz found Hoffman's lifeless body and called emergency services shortly before noon, sources told The Wall Street Journal.
Hoffman won the Oscar for best male actor for his role as Truman Capote in "Capote" in 2006, and he was nominated for an Academy Award three other times for "Charlie Wilson's War" (2007), "Doubt" (2008) and "The Master" (2012).