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(CNN)DNA testing led to the arrest of man in the 35-year-old killing of a girl in Rochester, New York, police and prosecutors said in an emotional press conference on Friday.

Wendy Jerome, 14, was raped and killed while delivering a birthday card in her neighborhood on Thanksgiving Day 1984 and her body was found by a pedestrian near a school dumpster that night with "obvious signs of trauma," said Rochester police Capt. Frank Umbrino.
Timothy Williams, 56, was arrested at his home in Melbourne, Florida, on Wednesday and arraigned as a fugitive, according to Monroe County Assistant District Attorney Julie Hahn.

In a tearful speech, Jerome's mother thanked the police department for the lengths it went to solve the case.