I have a situation in which one PC is sitting on top of a roof with a rifle (which I've house ruled as having stats of a repeating crossbow) and there is another PC approaching the building. He wants to literally snipe the other guy in the head as he approaches. Assuming the attack roll hits, is there any way this could be ruled as a 1-hit kill? The player is completely concealed and hidden and all that. Any advice would be greatly appreciated, I know 4th edition isn't super pvp friendly.
Probably not. Hit points are too abstract to illustrate death from damage to a sensitive spot, so unless his rifle deals enough damage to completely lower the hit points of the target below zero it's unlikely that he'd die from such a hit. And being that 4e Lacks any called-shots mechanic it'd have to be something that would be house-ruled into the game, which changes the scope of the question entirely.
There have been a few instances of people who have been shot in the head in real life that haven't died, so its just as likely that a fantasy character with access to magic and healing spells would be just as capable of surviving such grievous injuries.
In the event that the Rifleman did fire at the PC, rolled a critical hit, and exceeded the hit points of the PC he would die like any other player.
You should have decided this earlier
One of your players seems to have already committed to this, by setting themself up in a sniping position in order to attempt this manuever. In doing so, that player is acting on the belief (for some reason, probably verisimilitude based off real life) that shooting someone in the head at close range with their sniper rifle has at least very good odds of killing or otherwise incapacitating the target.
The other of your players probably is operating under the assumption that, having a very high number of hitpoints and not being in an encounter and furthermore being 'in town', in which case a one-hit kill from a weapon that normally does fairly low damage and should have a good chance of not 1-hit-killing the target even on a crit will seem completely unfair.
No matter who wins this conflict, both players will be unsatisfied, because the mechanism of resolving the conflict will seem unreasonable/arbitrary, and tacitly negate long-running actions/plans the players are undertaking. When the sniper first expressed this plan to you, you should have informed them that the plan will probably not work and is not something their character would think of as reasonable because (hp, no such thing as a vital area, etc), and instead (shooting him after he thinks a tough encounter is over, abandoning him to monsters in combat, etc) is the normal approach in this world. They're still free to try, but now they at least have been warned that this might be difficult and also isn't working the way they thought it would work.
You could have informed the other players, instead, that you are adding called shot rules and also sneak attack rules for people without access to the relevant powers and the bonuses include 'target is instantly killed regardless of hp, no save', and remind them that PvP is allowed in this campaign. However, doing so will remove the sniper's stealth advantage if you do it when the issue comes up, since it's pretty clear that the rules changes exclusively benefit their character, and that something PvP-y is coming up.
At this point, it is best to allow a retcon
Let the sniper know that the plan doesn't work the way they want because X reasons, and offer them the chance to not have done this in the first place.