Jessica Walker, aged 26, attended at the Accident and Emergency Department around 2.30am on Tuesday, December 24, but left the building via the main entrance at around 9.20am later that morning and has not been seen since.
She is described as white, around 5ft 4ins tall, medium build, with blond hair that was in a ponytail and speaks with a North East of England accent. It is believed that she may have recently moved from the Durham area.
Sergeant Jamie Harvey said: “We are increasingly concerned about Jessica and would ask anyone who may have seen her when she left the hospital to get in touch.
“In particular we are trying to find out what direction she went in after leaving the building, possibly towards the car park, or whether she might have taken public transport.
"Anyone who has seen Jessica, or who knows of her whereabouts, or Jessica herself if she sees this appeal, should contact us immediately on 101 and quote incident number 0896 of 24 December.”