Officers have been investigating sex abuse claims against Heath, who died in 2005 aged 89.
Their report released Thursday says "there is sufficient suspicion to have interviewed Sir Edward Heath under criminal caution regarding his suspected involvement in child sexual abuse."
Police looked at 42 allegations and said there was sufficient suspicion to have questioned Heath about seven of them. They include the alleged rape of an 11-year-old boy and alleged indecent assault on a 10-year-old boy.
Chief Constable Mike Veale of Wiltshire Police said the seriousness of the allegations made it imperative for police to investigate.
"There have been many views expressed as to whether the police should investigate alleged offenses committed by a deceased suspect," he said. "I believe this was the right moral, ethical and professional thing to do."
He said "a significant number of people" had made complaints about Heath.
"I hope people will understand that, given these circumstances, it would be an indefensible dereliction of my public duty as a chief constable not to have investigated such serious allegations against a former prime minister, even though he is deceased," Veale said.
Detectives made no judgment about the innocence or guilt of Heath, who was Conservative prime minister between 1970 and 1974.
Police said most of the alleged victims were boys from the ages of 11 to 15. The allegations date from 1961 until 1992.
The investigation began two years ago after Heath's name came up in a wide-ranging investigation of historical child abuse.
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