Tayside Police confirmed allegations against the former Top of the Pops presenter have been made by a woman living in the force area.
The widening investigation comes as it was revealed Savile’s headstone will be broken up and sent to landfill at the request of his family, out of
“respect to public opinion”.
It was also announced last night that the BBC is to bring in a figure from outside the corporation to chair its inquiry into complaints of sexual abuse made against Jimmy Savile.
The move came after police said they believe the “predatory sex offender” could have abused up to 25 girls over 40 years.
Details of the alleged incident against the woman now living on Tayside have been passed to Scotland Yard detectives who are said to be pursuing a total of 120 lines of inquiry in relation the former BBC disc jockey.
A Tayside Police spokeswoman said: “A disclosure has been made regarding a historical incident that happened in the Liverpool area. Full details will be provided to the Metropolitan Police, and support is being offered to the woman concerned.”
Savile’s family said they made the decision to remove the headstone to ensure the “dignity and sanctity” of Woodlands Cemetery in Scarborough.
The headstone, which bears the star’s image and lists his accomplishments, including the epitaph “It was good while it lasted”, has been taken to a stonemason’s yard in Leeds where the inscriptions will be ground away. It will then be broken up and sent to landfill. Funeral director Robert Morphit, of Joseph A Hey & Son, who organised Savile’s funeral and oversaw the dismantling of the headstone, said: “Yesterday afternoon the family contacted me and said they’d thought very carefully about the course of action with regard to the stone.
“They had decided that in order to protect the dignity and sanctity of this cemetery, it was appropriate to remove the stone.”
He said the stone was removed in three pieces and taken away. “We’ve taken it back to our yard in Leeds. We’ll grind the inscription off and we will dispose of the memorial. It’ll be broken up and just go to landfill.
“When we erected his headstone not three weeks ago, I expected it to be here forever. I never thought it’d be removed, let alone so quickly.”
The grave, in which Savile was buried at an angle so he could “see” Scarborough Castle and the sea, will remain unmarked for the foreseeable future.
The prime spot, which is roped off, was yesterday identifiable only by several bunches of flowers on a dirt patch.
Mr Morphit said once the family came to terms with the outcome of various investigations they would make a decision as to how it should be marked in the future.
In a statement, a Savile family spokesman said: “The family members are deeply aware of the impact that the stone remaining there could have on the dignity and sanctity of the cemetery.
“Out of respect to public opinion, to those who are buried there and to those who tend their graves and visit there, we have decided to remove it.”
A number of memorials to Savile have already been removed, including an inscription on the wall at Leeds Civic Hall in recognition of his charity work, and a street sign in Scarborough. A plaque outside his former home has been defaced.
Scotland Yard has formally recorded eight criminal allegations against the former star. The alleged abuse involves girls as young as 13 and includes two complaints of rape and six of indecent assault, with officers looking into up to 120 lines of inquiry, dating back to 1959.