Police are investigating claims that the former Rochdale MP, who died in 2010 aged 82, sexually abused boys at homes and hostels in the town.
The party's president Tim Farron said: "The party absolutely, as the Labour Party must also ... and, indeed, Rochdale civic society as a whole, need to answer serious questions as to who knew what and when."
However, he added that the police inquiry was the best way for the allegations to be dealt with.
Sir Cyril was alleged to have raped boys at the Knowl View residential school and abused boys at Cambridge House children's home, a private care home in his constituency which closed in 1965.
He was on the management board at Knowl View when he was a councillor and had a long association with the school.
The Crown Prosecution Service has said he should have been prosecuted.
Lawyers representing the alleged victims of the abuse are said to be considering legal action against the LibDems.
Last year, the LibDem leader, Nick Clegg, described the allegations against Sir Cyril as shocking and appalling, and said they must be investigated "to the bitter end".
However, he has recently faced criticism for refusing to launch an inquiry into what was known about his alleged behaviour by the party at the time.
Sir Cyril's family have said he always denied the claims when he was alive and they were saddened that allegations were being made.