What is the rank of the head of the field hospital medical department in a military district?

The concept is wrong. There is no such thing as a local army, both field and non-field armies are military series, there is no such thing as a local army.

Field hospitals are generally organized in regiments, while non-field hospitals are organized in regiments as a minimum, and above that there are divisional hospitals, such as the General Hospital of the Military Region (now the General Hospital of the Theater of Operations), the General Hospital of the Navy, the General Hospital of the Air Force, the 307th Hospital (the Hospital of the Academy of Military Medical Sciences), and so on. Higher than the division level of vice military or military level hospitals (because of the old change of level, a burst of vice military level, a burst of military level), such as the PLA General Hospital (that is, before the 301 hospital).

Field hospitals do not have a medical department, because they are regiment-level organizations, and the president and political commissar are regiment-level, and below that is the medical department, and the director is battalion-level. Only hospitals at division level and above are medical departments. The general hospital of the theater (i.e., the previous major military regions and military units) has a medical department head at the regimental level. The head of the medical department of the general hospital of the People's Liberation Army is at the level of a full division.