Carly Smith, 33, from Dewsbury, was picked up by CCTV cameras leaving St James Hospital, Leeds, on Wednesday and is pictured leaving the hospital grounds at about 7.21pm and was believed to be heading towards Harehills Road.
Officers say they are becoming increasingly concerned for Carly’s welfare and are focusing inquiries to find her in the Leeds area.
Det Chief Insp Steve Snow of West Yorkshire Police, said: “We are continuing our inquiries to find Carly and as time passes grow increasingly concerned for her welfare.
“She was captured on CCTV leaving St James Hospital at about 7.21pm on New Years Eve and may have been heading towards Harehills Road. I would appeal to anyone who saw her at the hospital or in the area nearby to contact us.
“Carly had been due to meet her partner on New Years Day but failed to arrive and it is out of character for her to be out of contact.”
Carly is described as white, about 5ft 1ins tall and of medium build.
She has dark collar length hair and was last seen wearing a white and grey speckled puffy coat, khaki leggings and dark shoes.
Mr Snow added: “We are continuing enquiries to find her both in Leeds and in her home town of Dewsbury. I would urge anyone who has any information about her whereabouts to contact Leeds District CID on 101.”