I don't believe this is an old railroad bridge. The adjacent line, which is the old Naugatuck Railroad main, is at a higher elevation. Secondly, this bridge is much wider than a spur line bridge would expected to be--twice as wide as the adjacent main line bridge. Since this used to be an industrial area, my vote would be a private industrial bridge to join buildings on either side of the river. At any rate, more research is needed.
I checked out some old aerial imagery. It looks like there used to be a spur line that curved off the adjacent rail line and crossed the river to serve a factory on Water Street.
I couldn't see any time that it was used for road use though, so I can't speculate as to when or why it was paved over.
I agree, more research is needed. But a quick thought on the width though, as I considered that as well: Since the line was operating on a curve, it would have to be wider to accommodate it. I've seen a few other examples in my time where a through railraod bridge was wider then normal to accommodate a curvature.
But either way it was definitely built for some use of the factory complex that was here.