Thanks for guessing, y'all! And Slaadi got as close as I could, identifying it as a Blow-fly, or Calliphorid.
The clue that identifies it as a fly is the pair of halteres: look between the belly and the last pair of legs; see the two little yellowish balls on stems? Those are what flies have instead of the second pair of wings. Other flying insects, like bees and wasps, for example, have two pair.
How Slaadi decided on blow-flies, I don't know. I had the same opinion, but I had an advantage; I'd seen the whole fly. It looked, from where I could see it on my window, like one of the black and blue flies that hang around our rhododendrons:
|It sort of looked like this.|
So, Slaadi; tell us. What did you see that said, "Calliphorid", rather than "Muscid", or something similar?
I've sent the photo in to BugGuide. I don't know if they can do any better, with just an underbelly. But I've been surprised by them in the past; they're amazing!