Is my tree killing these birds?

I have this weird tree in the middle of my yard. It’s a fruit tree of some sort that grows in all sorts of crazy directions (limbs wrap around eachother) and until I went crazy and chopped the heck out of it, the branches grew out and touched the ground. Like a weeping willow but with cherry tree branches.

Anyway, about a month ago I noticed a little dead bird (sparrow?) beneath it at the trunk. I happened to be walking by with a shovel so I hurriedly disposed of it before my dog could get to it.

Today I was in the yard again and found another bird. Face down, wings spread. Some sort of black bird with bluish-tinted head feathers (starling?). Dude was absolutely frozen solid with it’s eyes open and everything.

I didn’t have my shovel with me so I told the dog to “leave it” and ran to get one. She didn’t care the slightest about this dead bird. By the time I got back she was elsewhere in the yard. I don’t know how long the bird had been there (no maggots yet) but she’s outside all day by herself and didn’t touch it.

So this has me worried. There’s no windows around for the birds to run in to. I haven’t seen any cats around - no furry creatures except squirrels. The yard is fenced in. Since my dog showed no interest in the bird I feel like…er, I dunno…it was toxic? The dog knew it was poisoned?

Are perhaps the berries on the tree (definitely some kind of cherry - red fruit the size of a pea with a large cherry-pit-like-pit) poison for birds? Or am I just really paranoid?

I considered emailing the Audubon Society or the OSU Extension but today was trash day and I wasn’t about to freeze a bird corpse for them.

Two dead birds in the middle of my yard, though. Is that anything to be worried about?

West Nile Virus?
More on West Nile in Ohio.