The Daily Record is reporting a probe into police actions prior to the Trainspotting 2 star's murder last month is ongoing,
It is thought the investigation centres around a possible 'threat to life' notice issued to Mr Welsh in the lead up to his murder.
However, police at the time stated in a press conference in Edinburgh's Chester Street shortly after the murder that they weren't aware of any threat being made to Mr Welsh's life.
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The former Hibs casual and owner of Holyrood Boxing Gym owner was killed by a single gun shot to the head on the doorstep of his West End home on April 17.
Two arrests have since been made over the 48-year-old father of one's brutal murder, but both men have now been released.
Fake CCTV footage purporting to show the killer opening fire on Mr Welsh also circulated on the internet last week.
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A PIRC spokesperson said: "We are investigating the actions of the police prior to the death of Bradley Welsh.
"The matter was referred to the PIRC by the Crown Office and Procurator Fiscal Service."