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The Clallam County Sheriff's Office said Phillip Curtis Shelly, whose last known address was a Front Street motel in Port Angeles, said Shelly cut the satellite tracking device off his ankle at 6:50 a.m.
It was found in a postal drop box at the corner of Front and Laurel streets later in the morning.
Shelly has been known to hitchhike, and has shaved his beard in the past to avoid detection, the Sheriff's Office said. He may be headed to Graham in Pierce County.
Shelly is described as 5 feet 8 inches tall, weighing 140 pounds. He has brown hair and hazel-colored eyes.
He was convicted in 1998 of first-degree rape of a child, and was released with the tracking device in 1999, according to the Department of Corrections. He since has had minor violations of his court order, a spokesman said.
Anyone seeing Shelly is asked to call dispatch at 360-417-2459 or 9-1-1.