The Mental Health Clinic is a clinic down the road from the Antique Shop. Tim appears to be a patient there. No known name, staff, or other patients are ever stated, and the building is never seen from the front.
Tim never states what kind of mental health issues they are resolving, and the only appearance so far is Entry #53, so there is no solid conclusion as to anything regarding this clinic other than it specialize in mentality.
It is likely that the files that Jay found in Entry #60 and reviewed in Entry #60.5 are likely from this institution as they discuss the condition of Tim.