Are patients who are committed to the psych hospital allowed to refuse medical treatment?

Very complex issues. Any person may refuse medical treatment, even when committed to a psychiatric hospital. Yet these same people often do need medications. Legal perspectives cite 2 important bounds: protecting ill/vulnerable people, and not infringing on their autonomy. Therapeutic alliance between patient & doctor must walk between these bounds. In a medical emergency, the patient can be involuntarily medicated.
No. If a patient has been committed to a psychiatric hospital then he has been deemed a danger to him/her self or others. If that is the case then the patient would have to be treated involuntarily for safety reasons.