Ryan McEwan-King, 22, was sexually assaulted and strangled as she walked home from a pub in Northampton on Friday evening. Her body was found near a bowling green in the Racecourse park the next day.
Detective Chief Inspector David Armiger said it was possible that Miss McEwan-King had been attacked by someone she did not know who was lying in wait for her.
"Our advice, particularly to students, is not to walk in the vicinity of the Racecourse alone," he said.
"Clearly we have a killer on our hands and we are doing everything we can to find the person responsible for Ryan's death."
The fair-haired student, who was only 4ft 5in tall and weighed less than five stone, was due to graduate in two weeks' time.
She shared a flat with two other students who have been moved to other addresses for their own safety as police fear the killer may have a key to the flat.
Miss McEwan-King, from Nemphlar in Lanarkshire, was a music and drama student at Nene College in Northampton.
The youngest of five children, her parents Robin and Margaret McEwan- King said they were devastated by the murder of their daughter and spoke proudly of their "little girl with the big voice".
"She was such a professional performer. She had such a beautiful voice. You'll never hear that voice," said her father last night.
Holding back tears, Mr Mc Ewan-King, 54, said his daughter, had last visited home only two weeks ago to celebrate her birthday.
"We heard about this while we were at the Royal Highland Show ground at Ingliston where Margaret was showing sheep which Ryan had helped us to prepare," he said.
"We still don't know exactly what happened. We are absolutely devastated by this."
Miss McEwan-King last talked to her parents the night before she died.
"She wanted to know how we'd fared at the Shetland Sheep Championship and she was over the moon when she found out we'd won," he said.
"She had such a wonderful rapport with animals and she had helped prepared the sheep for the show."
The family moved to Lanarkshire five years ago and Miss McEwan-King had just started a part-time job at Marks & Spencer. She had hoped to become a professional singer.
Her father said: "Music was her first love. She was extremely gifted."Reuse content