Michael Errington is currently serving 18 years in prison for manslaughter and has spent the last nine years living at The Priory Hospital in Darlington.
The 51-year-old left the unit four days ago on approved leave from the premises and did not return.
Police have issued a ‘do not approach’ warning over the missing man who caught a train to Edinburgh, arriving into Waverley at 2.38pm on Saturday where he was captured on CCTV getting off the train.
He is on medication, which police believe he has not taken since Saturday. Without it he can become aggressive and unpredictable.
Members of the public are being warned not to approach him if they see him, but call Durham Constabulary immediately on 999.
After leaving the hospital, Michael caught a bus into Darlington town centre. Once there he caught another bus to Durham, and then a further bus to Newcastle where he boarded a train to Edinburgh.
Upon arrival he then left the station via the Princes Street exit and turned left towards the castle.
Michael is described as being around 6ft tall, of medium build, bald, with tattoos on his arms and legs. He was thought to be wearing a red polo shirt, but may have changed into a grey t-shirt. He may also be wearing a black jacket, light blue jeans and white trainers.
Temporary Superintendent Catherine Clarke, from Durham Constabulary, said: “These are our last known sightings of Michael. Due to his mental health issues, which can become exacerbated when he hasn’t taken his medication, we believe he may pose a risk to the public.
“Therefore, we would urge anyone who sees him not to approach him but to call us immediately on 999.”