Mary spotted this critter atop the roof and, much to my surprise, it waited courteously until I deployed the camera:
It looks, walks, and acts just like a pigeon:
… but we’ve never seen one with those feather patterns & colors. It’s not in any of our books, so it may be an escaped domestic pigeon.
Those feathers require plenty of body maintenance:
As nearly as we can tell, it’s wearing a green leg band with three digits that might be 904:
If this was your bird, it flew through Red Oaks Mill NY just after noon on 1 May 2017 …
The Smell of Molten Projects in the Morning 
Looks like some racing pigeons I’ve seen. We have a spectacular range of pigeon colours here, likely coming from a flock of fancy Indian/Afghani pigeons that were released by their owner about 15 years ago. The males used to do the whole tumbling courting display (fly really high with lots of attention-attracting wing clapping, then plummet down, wings folded in and tumbling, then pull out close to the ground) but I haven’t seen that in a while.