I believe our sidewalks are maintained by the city. Someone came by a few years ago and ground off the edges of a few slabs where they were out of alignment to make them level again. I didn't call anyone or pay anyone to do that, so I presume the City of Norman did it of its own volition.
That said, I believe that initial construction of sidewalks is to be done by the property owner when the property is initially improved. There are a few lots in subdivisions that for whatever reason never had houses built on them. The sidewalk stops at the boundary of those lots and starts up again on the other side of them. That really blows when it's been rainy and you have to walk through mud or walk in the street. I can't imagine people in wheelchairs or that use walkers find it easy to deal with, either.
While not really sidewalk-related, a really annoying situation came up in the last rental house I lived in. That house had a street behind it rather than another property. So behind my back fence was a sidewalk and a 7-foot grass strip, then the street. I had no idea I was responsible for its maintenance, since it wasn't really accessible from the rest of my property, until the city sent me a nastygram complaining that the grass was too high. So I had to push my lawnmower all the way around the block to mow this stupid 7-foot grass strip. If I had owned that property, I probably would have seen if I could tear the grass out and install pavers or something like that.