Scottish police are investigating claims that Lord Janner abused a teenage boy in the country in the 1970s.
The decision by Police Scotland to look at the allegations – made almost a quarter of a century ago – comes two months after the Crown Prosecution Service in London decided not to charge the peer over similar claims.
Alison Saunders, the director of public prosecutions, said the 86-year-old was not well enough to stand trial as he is suffering from severe dementia.
But the new investigation, under Scotland’s independent legal system, renews the prospect that the former Board of Deputies president could face criminal proceedings.
It is alleged that Lord Janner sexually abused a boy after travelling to Scotland with him. The alleged victim complained to police in Edinburgh in 1991 but Scottish prosecutors say they were never told of the case.
Following the CPS decision in April, Scottish detectives are said to have trawled files for details of the 1991 claim.
A senior officer at Police Scotland confirmed officers were investigating an historical complaint.
Lord Janner, who has held numerous communal leadership roles over the past six decades, has repeatedly denied any wrongdoing.
His lawyers and family said in a statement after the CPS decision that he was "a man of great integrity and high repute with a long and unblemished record of public service".
A lawyer representing alleged victims said civil claims against him would be pursued regardless of the actions of prosecutors.
An independent QC is reviewing the CPS decision, and lawyer Liz Dux said she would pursue a “series of individual claims” on behalf of alleged victims once the review was complete.