Ledger was found dead in his bed at his apartment on Broome Street, Soho, in Manhattan, by his housekeeper about 3.35pm local time.
Ledger's body was removed from his New York apartment and wheeled into the back of a medical examiner's van.
"It's all preliminary at this stage," Officer Brown said.
"We had a call for an unconscious male at 421 Broome Street.
"At 3.26pm [New York time] we got to the scene and there was an unconscious male.
"We called EMS [ambulance] to the scene and EMS pronounced the unconscious male dead.
"Preliminarily, it is believed it is the actor Heath Ledger."
Police officers stood guard at the Soho apartment building as a crowd of photographers gathered outside.
Asked about reports of the pills in Ledger's apartment, Brown said: "I can't confirm that but I've heard the same thing."
Ledger was taking sleeping pills after completing I'm Not There, in which he played one of the many incarnations of singer Bob Dylan.
He told The New York Times in a November interview that he "stressed out a little too much'' during the Dylan film, and had trouble sleeping while portraying the Joker, whom he called a "psychopathic, mass-murdering, schizophrenic clown with zero empathy".
"Last week I probably slept an average of two hours a night," Ledger told the Times.
"I couldn't stop thinking. My body was exhausted, and my mind was still going."
He said he took two Ambien pills, which only worked for an hour, the paper said.
