Police were alerted following his escape, but Inspector Baker - in charge of overseeing the force's 999 emergency response - is said to have assessed Matthew as being at "medium" risk of serious harm.
The Independent Office for Police Conduct has recommended West Midlands inspector Colin Baker should face disciplinary action over the 2020 death of Matthew Caseby, 23.
It meant a full-scale search was not carried out despite police being aware of Matthew's mental health history and their logs stating he had threatened self-harm at the hospital before his escape.
The police watchdog launched an investigation into police actions following a complaint from Matthew's family.
"We decided that a police inspector should attend a misconduct meeting in relation to their decision making and handling of information after Matthew was reported missing.