IN JUNE 1962, three inmates shimmied through a hole they’d chiselled into the walls of Alcatraz prison and climbed up to the roof.

To mask their escape, they’d placed in their bunks realistic-looking dummy heads they’d made out of papier-mâché and human hair from the prison barber shop. The three men — brothers John and Clarence Anglin and fellow inmate Frank Morris — grabbed makeshift paddles and plunged an escape raft they made of stolen raincoats into the dark waters of San Francisco Bay. Alcatraz officials have long stated that the men drowned, maintaining the prison’s bragging rights of no escapees. But now, more than 50 years later, new leads are being presented by the Anglin family, who are cooperating with authorities for the first time. They claim that not only did the brothers survive the escape, they were alive and well up through at least the mid-1970s — and may still be alive today. The evidence is offered up by the Anglins’ nephews David, 48, and Ken Widner, 54, who are featured in Alcatraz: Search for the Truth, a History Channel special about to air in the US. The evidence has pumped life into the cold case, and has investigators lining up new interviews and planning to search South America for signs of America’s most notorious escapees. “This is absolutely the best actionable lead we’ve had,” Art Roderick, the retired US marshal who was lead investigator on the case for 20 years, tells The Post. The Anglin family sat on those leads for years because, they say, they were spied on and harassed by the FBI for years. But a desire to see the case solved before Marie Anglin Widner — the Winners’ mother and the escapees’ sister — passed away, combined with the cockiness of Alcatraz officials, inspired them to come forward. “[Alcatraz officials] were not willing to ... say, ‘Maybe [the escapees] did make it’, ” David Widner says. “That gave me the motive to prove them wrong.” First there were the Christmas cards, signed with Clarence and John Anglin’s names, that were delivered to their mother during the three years after the escape. They arrived without postage. In the History Channel special, the nephews take the cards and other evidence to Roderick, who retired in 2008 but is still working on the case. Though the handwriting matched, the investigators were unable to pinpoint the exact date of the cards. But the nephews also came forward with a photo — which will be revealed on the show — that proves the Anglins may have been alive in the 1970s. That really caught Roderick’s attention. “When you work these types of cases there’s a feeling you get when stuff starts to fall into place,” he says. “I’m getting this feeling now.” The next big piece of evidence was buried — about two metres in the ground. The family finally let investigators dig up the remains of the Anglins’ other brother, Alfred, who was electrocuted during his own escape attempt from an Alabama prison. They needed his DNA: Authorities had discovered a set of bones that washed ashore north of San Francisco in 1963, which they said may have belonged to one of the escapees. But the DNA proved to not be a match, bolstering the Anglin family’s claims that the two may indeed still be alive. (The bones could still belong to Morris, though; he has no living relatives to test.) David Widner says he’s working on a book that will contain more evidence not included in the TV show. That includes a surprise guest star: Boston crime boss Whitey Bulger, who met the future escapees in Alcatraz. Bulger, in a 2014 letter to Ken Widner, said he instructed John and Clarence on how to navigate bay currents, and dropped a key piece of advice about being a fugitive. “He taught them that when you disappear, you have to cut all ties,” Ken says. “He told me in a letter, ‘This is the mistake that I made.’ He told me, ‘These brothers undoubtedly had done exactly what I told them to do.’ ” The nephews hope the special rewrites the history of Alcatraz, and cements their uncles and Morris as the only people to successfully escape the island, out of the 36 who tried. Roderick has lined up 10 new interviews since seeing the evidence, and is talking to US Marshals about investigating in Brazil, where the Anglins may have ended up. If they are still alive (both would be in their mid-80s by now), international laws may not even allow extradition to the US. Nonetheless, Roderick would want to sit down with them to figure out how they did it. If they died and their bodies can be found, however, Ken and David want to bring the Anglin brothers back to the family plot in Ruskin, Fla. Says David, “We should get ’em a place ready.” This story originally appeared on the NYPost.