Daisy Preston, aged 11, was found unresponsive by paramedics at a small children’s play area near Sycamore Gardens at around 1.45pm on Sunday June 3.
She was taken to the Royal Lancaster Infirmary where she was sadly pronounced dead a short time later.
DCI Jill Johnston said: “This is a terribly sad and tragic event and our thoughts remain with Daisy’s family at this extremely difficult time.
“They are being supported by specially trained staff from a number of agencies.
“The cause of Daisy’s death is not yet known and remains under medical investigation.”
Anyone with information should call 101 quoting incident reference 817 of June 3.