Got bored and looked it up, and there aren’t, surprisingly. At least not in the 2019 revision of the Major League Baseball rules. But they do define what a ball is, and isn’t, and a baby is not considered a valid ball (3.01).

But at least according to Rule 5.01©(1), if part of the baby gets on the batter, they might be considered “hit by pitch”, and therefore eligible to advance to first base. (It would be considered a ‘dead’ ball, which is funny, given the context.)

The rules aren’t written expecting the ball to break into bits upon impact, so it’d depend on it actually happening to get precedent.

But at least going by 4.01(a,e), it’s the umpire’s fault for providing an invalid “ball”, and they might have to clean up, since they’re tasked with replacing the “ball” if damaged.

I would assume the baby’s head is what counts as the ball, here. If it detaches in a large piece and leaves the stadium, it should likely count.

Do they have spare Christian babies on hand though?