In the 911 call from Lovato's house -- obtained by TMZ -- the caller remains calm while taking orders from the dispatcher. As the ambulance approached, the dispatcher let the caller know they'd soon hear sirens to which the caller responded, requesting they be shut off ... seemingly to keep the situation private from neighbors. However, the dispatcher says that's just not possible.

We broke the story ... Demi was rushed to an L.A. hospital after suffering an overdose, which law enforcement believed was from heroin. However, a source close to the singer said it wasn't heroin, but refused to divulge the source of the OD.

Demi's emergency came after an all-night party that started with a birthday celebration for one of her backup dancers at Saddle Ranch in WeHo.

As we reported ... Lovato had been struggling with drugs for weeks, even before last month's public confession of a relapse on her song, "Sober."

Check out the initial dispatch audio (below). You hear the dispatcher for the L.A. Fire Department calling LAPD and saying, "I thought maybe you guys better go on something like this." It's unclear if he's saying the LAPD should go out because Demi is a celebrity, or because of a drug overdose. The call is redacted, so we don't know if Demi's name or the OD was mentioned.