> If you know the dummy was overlapping you know it was mouse.
What if it's a touch and the mouse cursor just happened to be in the same spot?
That would mean that the user is dragging while touching, so I guess you could check that its speed is zero or pretty close, and/or mouse is down.
The number of corner cases is just going to balloon if you insist on working both in at the same time. Plus the logic for UI over the entire screen is vastly different between the two, especially if you want zones where the user can click on both UI, and background.
Letting the user decide and have events for both may be the best method.