If you have the means to put it out of it's misery, well then I say you do it.
Any state that has laws preventing a citizen from doing that common sense decent thing has lost it's way.
There are many places in states/cities where it could take several hours for a sheriff or policeman to respond to such a call.
If all you have is a sharp hunting or fillet knife cut the aortic arch or carotid arteries from top of the breast bone (sternum) the pointing the knife blade in at a 60 degree angle and out through both side of the lower neck.
Then I'd field dress it and see that it was cooled down and made us of by someone. Maybe you can't get into the field dressing in business clothes. But I'd think that someone who wasn't would stop and give you a hand and share the meat with them or a food shelf.