The allegations were made in a recently published book by Rochdale's Labour MP Simon Danczuk, who claimed the town's former Liberal Democrat MP raped a number of young boys at a residential school.
Police, spies and politicians helped to hide the historical child abuse carried out by Smith, according to Mr Danczuk's book Smile For The Camera: The Double Life Of Cyril Smith.
The 29-stone politician was left free to abuse children as young as eight despite 144 complaints by victims, he and co-author Matthew Baker said.
Rochdale Council has appointed a deputy high court judge to independently look into claims that sexual or physical abuse of children took place at premises owned, managed, operated or funded by the council from 1961 to 1995.
It will also look into the activities of council officers or employees, councillors and council-appointed school governors who were involved with those premises.
During the 1960s, Sir Cyril, when he was a local councillor in the town, acted as a governor for several schools and was active on many council committees involving youth activities.
GMP chief constable Sir Peter Fahy said:"I would just like to point out that investigations into abuse are extremely difficult. They do take a long time because of, often, the damaged effects on the particular victims and the need for corroboration.
"But we are determined to do a very thorough investigation and obviously when we are carrying out investigations into abuse at institutions, clearly we look at the liability of those who may have been running those institutions."