Ali Rajabpoor, 24, was last seen on Thursday 2 March, when he failed to return to Forest Lodge hospital unit in Sheffield following his weekly agreed leave from the hospital.
Mr Rajabpoor was placed indefinitely at the hospital in 2015 following his conviction at Leeds Crown Court for an offence in West Yorkshire the same year.
Police have advised members of the public not to approach Mr Rajabpoor and to contact officers if you see him, as he may pose some risk to the public.
He has been described as around 5ft 10incs tall, of a slim build, with short dark hair and to have been wearing a blue top with a red zip, a grey hooded top with white writing on it and to have a distinct gap in his left eyebrow.
Police have said that extensive enquiries have been carried out since he was reported missing and these are continuing.
If you have any information about the whereabouts of Ali or have seen him, please contact police on 101 quoting incident number 722 of March 2.