Detective Chief Inspector Paul Fotheringham's full statement said:
Following recent speculation in the media, I would like to make it clear that Thomas Cohen is not in any way under suspicion of any involvement in Peaches Geldof-Cohen's death or our concurrent investigation into the supply of drugs.
He has not been arrested or interviewed under caution and there is no plan to do so.
The only statement he has provided related to his discovery of Peaches' body, which is a standard requirement.
We are in regular contact with both sides of the family to keep them apprised of our progress.
Our investigation into the supply of drugs is continuing and remains a live investigation.
Inaccurate reports have also been made suggesting that no drugs paraphernalia was found at the address, with suggestions that the scene had been 'tampered' with prior to police arrival.
While no detail will be provided around specific items, to prevent further speculation I will confirm that contrary to rumour in the media my officers did seize drugs paraphernalia from the address on 7 April.
The coroner has authorised the disclosure of this information.
Our investigation on behalf of the coroner continues and there will be no further information released at this time.
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On Friday, police said it appeared the girl had shot herself in the face with the weapon.