Published Friday, 02 May 2014
Geldof's body was found at her home in Kent, England by her husband Thomas Cohen on 07 April.
An inquest on Thursday was told that results of toxicology tests revealed traces of heroin in her blood at a level which meant it was "likely" to have contributed to the tragedy.
Detectives are now probing how Geldof, daughter of musician Bob Geldof, obtained the drug.
A Kent Police spokesman said: "We can confirm an ongoing investigation into the supply of drugs in connection with the death of Peaches Geldof."
The representative added that there have been "no arrests and no interviews under caution".
The inquest is due to resume on 23 July.