Last Bus to Woodstock by Colin Dexter

Beautiful Sylvia Kaye and another young woman had been seen hitching a ride not long before Sylvia's bludgeoned body is found outside a pub in Woodstock, near Oxford. Morse is sure the other hitchhiker can tell him much of what he needs to know. But his confidence is shaken by the cool inscrutability of the girl he's certain was Sylvia's companion on that ill-fated September evening. Shrewd as Morse is, he's also distracted by the complex scenarios that the murder set in motion among Sylvia's girlfriends and their Oxford playmates. To grasp the painful truth, and act upon it, requires from Morse the last atom of his professional discipline.