- University Circle Police - a private department funded by the businesses they serve. University Circle is a neighborhood housing many significant educational, medical, cultural and historical facilities, which is bordered on all sides by very high-crime neighborhoods
- The Transit Police, which I believe may be the largest department in Ohio - polices the public transit buses, trains and terminals
- CMHA Police - serves the public housing projects in the county
- CMSD Police - serves Cleveland's public school district
- Cleveland's three largest hospitals, Cleveland Clinic, University Hospitals, and MetroHealth, each have their own police forces (though apparently not web sites)
- Metro Parks Rangers - basically park rangers with police authority
- Most of the colleges and universities in the area (even the small schools and technical colleges) have their own campus police forces
That's obviously in addition to all the private security services that lack full law enforcement authority. And I'm probably leaving a few out in my list above - it's been a few years since I've lived there or payed real close attention. But the point is, it's by no means unusual for a private organization to form it's own full-fledged police force.