As far as I know, there's no automated tool to identify the resource hogs in your scene. You'll need to do most of it manually. But surely you'll have an idea on what object / element could be the cause? Like, high res textures, dense meshes (check subsurf and multires modifier render settings too!!), lots of copies instead of instances, or fur / hair.
One possibility is to put those objects on separate layers, and render just that layer with very low samples (1 should be enough). The memory consumption can then be read in the debug print line on top of the render view.
Important: Use final render (F12), as many modifiers (like the Subsurf by default) have higher settings for final render than for vieport render.
For rendering animations, it might also be beneficial for debugging this to have the memory usage in the test render frames directly. You can enable Stamp Output and check Memory to do so, if you have Blender 2.78 (or a current development build which was compiled after Jul 14, 2016):