Jed Allen, a groundsman who took care of the prestigious university's parkland, is believed to have fled after stabbing Janet Jordan, 48, sister Derrin, and stepfather Philip Howard, 44, at their home in Didcot in Oxfordshire over the weekend, police said.
The three bodies were discovered in a house in Didcot, Oxfordshire, after officers were called by a member of the public on Saturday night.
Thames Valley Police had closed Oxford University Parks in search of the suspect who has a distinctive black spider tattoo on his left hand, described as white, is about 1.8 metre tall and stocky.
"It is vital that we trace Jed Allen and I would urge anyone who has any information about his whereabouts to contact police. If you see Jed please do not approach him, instead call 999 immediately," he said in a statement.
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"He's worked for a couple of years for Didcot Town Council and has been calm, has been working in the parks and has been fine. Studying at Abingdon and Witney College, a normal person," Didcot town councillor Margaret Davies said while describing Allen as calm and normal.
Ladygrove Community Centre, next door to the school, is opening its doors to allow staff, children and families to pay tribute to the little girl.