Raymond Rattray, 22, was struck and killed while walking on the shoulder of the southbound lane of Route 208 just after 5 p.m.
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Police discovered his body approximately 20 feet from the road near Hawk Drive and Cross Creek Road on Wednesday afternoon.
Authorities said the victim, who is from New York City, was struck by a dark-colored sedan traveling south.
The vehicle fled the scene, but police believe it sustained damage to the front-end passenger side.
School officials say Rattray was a senior philosophy major in the Educational Opportunity Program and a member of the Men's Rugby Club.
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Anyone who may have witnessed the crash or have information is asked to call the Ulster County Sheriff's Office. To speak with a detective, call (845) 338-3640 or call a confidential tip line at (845) 340-3599.
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