The Independent Police Complaints Commission said it had received an allegation "that a criminal prosecution was not pursued, when a person threatened to expose that Sir Edward Heath may have been involved in offenses concerning children."
The Wiltshire Police force said it was trying to find "witnesses or victims who support the allegations of child sex abuse," and urged victims to come forward.
Heath, a Conservative, was prime minister between 1970 and 1974 and had a home in Wiltshire county. He died in 2005, aged 89.
A dam of official silence around child abuse in Britain began to break after the 2011 death of entertainer Jimmy Savile, when dozens came forward to say he had abused them. Subsequent revelations have implicated other entertainers, as well as clergy and senior politicians.
New Zealand judge Lowell Goddard, who is leading the public inquiry, said last month that Britain had been stunned by revelations about child sexual abuse, and warned that the true scale of the crime has long been underestimated.