Wikimedia Refuses to Take Down Monkey Selfie
petapixel.com
petapixel.com
However, the photographer isn't his best defender - he goes on about the expense of the camera and lenses "he used for his trip" - when in reality, as a professional photographer, it's highly unlikely he purchased those tools to create this specific image (because of course he didn't have that intention), and it's disingenuous to act like he's out the cost of the photography equipment by not being able to claim royalties on this one image.
I would argue NO, from a common sense standpoint, but the law isn't really about common sense.
If he had accidentally constructed a situation where the monkey's pressing a button killed someone, we would consider it some kind of negligence or manslaughter (a much weaker claim) on his part, and the monkey would probably not be blamed.
You're also assuming that the ability to be held liable for murder and the ability to hold copyright are satisfied by the same criteria.