Yes, I called animal control. They didn't want to examine it, but did say they'd come pick it up if I put it at the curb. I used a shovel.
We're not directly responsible for her death--i.e., we don't do anything to kill wildlife--we just prevent them eating our livestock. So I don't really feel all that guilty, just a little sad for her. I do think she was sick--she was scruffy around the neck & there was "scat" in several locations nearby, including some still attached... which makes me think it may have been a traumatic death, but I can't imagine what would have done that to her and then left her there. So disease is still probably the cause.
Anyway--she's a beautiful animal and it was interesting to get a close look, though of course we didn't actually handle the body. She was still limber when I picked her up with the shovel, so she can't have been dead all night--it was 15 degrees out there last night. Interesting, anyway.