According to a report in The Sun, the allegations relate to Edinburgh City Mortuary on the Cowgate, in the 1990s.
The paper quotes someone who claims to be a former worker at the mortuary, who said that some other staff members openly talked about abusing both male and female corpses.
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The person said that the recent news that David Fuller, 67, molested at least 100 dead bodies in Kent hospitals made them want to report the alleged incidents in Edinburgh.
The un-named source told The Sun: “When I was working at the mortuary some of the staff members said they had sex with the bodies at night.
“They told me it didn’t matter if they were male or female.
“At the time I just put it to the back of my mind but the news brought it all back. That’s why I went to the police. I had to report it to clear my conscience.”
A Police Scotland spokesperson confirmed that a report had been received and that the force is investigating.
The spokesperson added: "We are aware of a report. Enquiries are ongoing and at an early stage."
Last week hospital electrician Fuller admitted murdering then sexually assaulting two women decades before carrying out dozens of sex attacks on corpses in mortuaries.
He filmed himself carrying out the attacks at mortuaries inside the now closed Kent and Sussex Hospital and the Tunbridge Wells Hospital, in Pembury, where he worked in electrical maintenance roles since 1989.