The autopsy on Peaches Geldof, who died suddenly aged 25, has proved inconclusive, as police continue to await the results of toxicology tests.
Peaches, who wrote for British magazines and newspapers and presented celebrity-driven television shows, was found dead at her countryside home on Monday.
The local Kent Police force in southeast England said her death was being treated as "a non-suspicious, unexplained sudden death".
"A post-mortem examination held on Wednesday following the death of Peaches Geldof has proved inconclusive pending the result of toxicology analysis," police said in a statement.
"Officers continue to investigate the circumstances surrounding the death in order to compile a report for the coroner. "The result of a toxicology report can take several weeks."