Former Liberal MP Sir Cyril Smith was accused of abusing young boys in Rochdale during the 1960s, in a statement by Labour MP Simon Danczuk in the House Commons.
A Lancashire Constabulary spokesman said they were not planning to investigate the matter as there are no current allegations pending.
It said: "We believe there was an investigation in the late 1960s but as no records are now held it cannot be ascertained whether a file was passed to the Director of Public Prosecutions."
Police say they are "now publicly acknowledging that young boys were victims of physical and sexual abuse committed by Sir Cyril Smith".
Former Liberal MP Sir Cyril Smith was accused of abusing young boys in Rochdale during the 1960s, by Labour MP Simon Danczuk in the Commons