The cities would have been responsible for building sidewalks to the bridge. If you look around where the bridge is on modern maps you'll see that a lot of the residential area on the North side of the bridge (Richfield) just doesn't have sidewalks.
It's even weirder than that! Residents of Richfield at the time saw the lack of sidewalks as a feature, not a bug. They wanted to distinguish themselves from Minneapolis, so they protested the building of sidewalks because "how would people know we are a suburb if we have sidewalks?" (This is a real quote from a real, very politically active resident at the time. Seriously.)
