I asked that question recently, and the answer I received was that if a person got bitten by a snake, someone in the party should kill it to show the medical personnel so as to get the correct antivenin.
Slightly left of topic, but please don't do this.
1) Severed snake heads can still bite and envenimate. It is a reflex action and does not require a live brain. You never want to generate a second victim in order to help the first one.
2) Bring a dead or half dead snake to an ED and they are going to freak. Seriously. I've been there when it happens.
3) At least in Northern Mexican, the US and Canada, there are really only two basic antivenins. Almost all bites are going to be crotalids (pit vipers). There is a polyvalent antivenin that covers all of these. For the extremely rare coral snake bite, the antivenin is rarely needed and almost impossible to get. So the decision is usually if a person will be treated and not with what antivenin. In rare cases where it is unclear, s few quick questions will differentiate. Most snakes in the US are not venomous anyway.
4) If you can shoot it with a gun, you can shoot it with a camera. The pictures are then easily sent to someone who can actually identify the snake. Few Emergency Physicians can reliably identify a snake. Once you mangle the head, many distinguishing features are lost. Then you need someone who can do it based on coloring.
5) There are plenty of snakes on the endangered species list. Taking out a harmless one for ID purposes, could have you trying to keep yourself out of club Fed.
So, in short. Unless it is going to hurt you, don't shoot it. And don't shoot it, then bring it to the ED.