Is the city supposed to clear its sidewalks? Or just the residents?

I think I've seen a requirement for residents in our city (Upper Arlington, Ohio, a suburb of Columbus) to clear their side walks after a snow storm. We haven't had the snow that the northeast or west of Chicago have had, but we get 2-3 inches from time to time. Today I noticed that when driving west on McCoy Road, all the sidewalks on the south (residential) were clear, and all the sidewalks on the north (Thompson Park) were icy and snow covered and dangerous, because that's where people go to walk.