David Burke, 37, left St Andrew's hospital in Northampton on Friday afternoon with another patient, who has since been found in Birmingham.
Mr Burke was thought to be in the West Midlands area, possibly Birmingham or Coventry, the West Midlands force said.
It said people were advised not to approach him but to call police. Mr Burke has been described as white, 5ft 7in tall and being of stocky build.
He was wearing a yellow and black horizontal striped T-shirt and blue tracksuit bottoms with yellow stripes down the side.
Police are looking for a mentally ill man who has absconded from hospital.