Detective Chief Inspector Paul Fotheringham told a hearing in Gravesend, Kent, on Thursday that "recent use of heroin and the levels identified were likely to have played a role in her death."
On April 7, Geldof's husband, Thomas Cohen, found her at their country home in Kent, where she was taking care of their 11-month old son, Phaedra.
"It was obvious to him that she was deceased. She was located on the edge of a bed with one leg hanging down to the floor with the other leg tucked underneath her; she was slumped forward across the bed," Fotheringham said. "Thomas called for his mother and they quickly located Phaedra and called the emergency services."
Though Geldof had a party-girl past, she said she had given up her "wanton" lifestyle when she became a mother.
Police said they found no evidence of drug use or paraphernalia at the scene of her death. Though authorities initially described her death as "unexplained" and "sudden," they will now look into the possibility that someone cleaned up before they arrived.
They will also investigate the origin of the drugs.
“We can confirm an ongoing investigation into the supply of drugs in connection with the death of Peaches Geldof," Fotheringham added.