Eileen Barrott, aged 50, was found with serious injuries in Naburn Fold at 6.31pm on Sunday, August 15.
She was pronounced dead at the scene.
Her death is being treated as murder.
Officers are now trying to trace her husband Mark Barrott, 54, who travelled to Scotland yesterday.
Enquiries have shown Mark Barrott left Leeds railway station by train at 1pm yesterday.
He arrived at Edinburgh Waverley station at 4pm.
West Yorkshire Police have released CCTV images of him at Leeds railway station yesterday along with an image of him taken in 2015.
Investigating Officer, Detective Chief Inspector Vanessa Rolfe said: “We urgently need to speak to Mark Barrott in connection with the investigation, and we are keen to hear from anyone who has seen him or who has any information that could assist in tracing him.
“He was last known to be at Edinburgh Waverley station at 4pm yesterday and we would like hear from anyone who saw him then or since, or who can assist in establishing his current whereabouts.
“We would advise members of the public not to approach him but to contact the police immediately via 999 if they do see him.”
Officers are also appealing to trace Mr Barrott’s car – a silver Toyota Avensis, registration FJ51 ZHB - which is still believed to be in Leeds.