Heath was Prime Minister between 1970 and 1974 and leader of the Conservative Party from 1965 to 1975 when he lost the leadership to Margaret Thatcher. He died in 2005 at the age of 89.
The Independent Police Complaints Commission (IPCC), said the claim of child sexual abuse had been made to Wiltshire police in southwest England, where Heath lived for much of his life. It gave no details of the alleged abuse nor of the complainant.
"This is an investigation into allegations Wiltshire Police did not pursue a criminal prosecution when a person threatened to expose that Sir Edward Heath may have been involved in offences concerning children," the IPCC said in a statement.
The IPCC will also examine whether Wiltshire Police subsequently took any steps to investigate the claims.
Wiltshire police said it was carrying out enquiries to identify if there are any witnesses or victims who support the allegations of child sex abuse.
"Sir Edward Heath has been named in relation to offences concerning children," it said. "He lived in Salisbury for many years and we would like to hear from anyone who has any relevant information that may assist us in our enquiries or anyone who believes they may have been a victim."
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