Kent police said there was an "ongoing investigation into the supply of drugs" in connection with her death on April 7.
Geldof, the second daughter of Irish singer-songwriter Bob Geldof, was found dead by her husband, Thomas Cohen, in a spare bedroom in their home.
Toxicology tests showed she had heroin in her system, an inquest heard yesterday.
Detective Chief Inspector Paul Fotheringham said: "Recent use of heroin and the levels identified were likely to have played a role in her death."
"There have been no arrests at this stage," the BBC reported.
Geldof's mother, TV presenter and writer Paula Yates, died from a heroin overdose at her London home, aged 41, in 2000.
At the inquest, Fotheringham described how Geldof's husband had tried to make contact with his wife before he found her body.
Cohen, a musician, had been away for the weekend with the elder of their two sons, Astala, leaving Geldof at home with their 11-month old son, Phaedra.
An initial post-mortem did not establish a cause of death and further toxicology tests were ordered. Those tests confirmed the recent use of heroin, police said.
None of the Geldof family attended the hearing, which opened and closed within 10 minutes. Coroner Roger Hatch adjourned the inquest for a full hearing to take place on July 23.
Geldof had spoken openly about her struggle to deal with her mother's death - and of experimenting with drugs in her teenage years - but had cited motherhood as a central part of her "healing" process.
She left home at 16 and went on to contribute to the Telegraph and the Guardian, as well as TV shows including ITV2's OMG! with Peaches Geldof.
She also worked as a model and, just last week, attended a launch for Tesco's F&F clothing range in London.
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