Dictionary:

semipublic

  (sĕm'ē-pŭb'lĭk, sĕm'ī-)

1. Partially but not entirely open to the use of the public: prohibited smoking in public and semipublic places.
2. Partially but not totally owned by the public: a semipublic utility company.
3. Open to the knowledge and judgment of only a part of the public.

The adjective has one meaning:

Meaning #1: having some of the features of public institution