To hang or not to hang...

I don't know how many of you have read Perry Mason books but if you get a chance I would recommend you to give it a try. I have read most of the series and I enjoyed them thoroughly. A couple of days back while watching some comedy on TV, the host interviews a Perry Mason impersonator (btw, Perry Mason was a fictional character like Sherlock Holmes). The host begins by uttering the usual salutations and then says,

"Perry, I always wanted to ask you this. Now, suppose a thief happens to enter a house to commit robbery. But ends up being pushed into a corner by the house owner. In this predicament the thief takes out his gun and shoots the owner. The bullet hits the owner right in the head but he doesn't die. Instead the owner goes into a deep coma and becomes a vegetable. A whole year passes and the family of the house-owner realise that the victim is 'brain-dead' and decide to pull the plug from the life support system. The question is this: Does the thief face the charges of 'murder' or an 'attempted murder'?"

Of course this was asked by the comedy show host to put Perry Mason in a fix, and make the audience laugh. But to me its more than just humour. I wonder what the correct legal position on such a case is. Any of you have any idea(s)?