I imagine that if this happens a Dungeon Master will contact the other player and ask him or her to respect the outcome and leave it be.Absurd as it sounds, they wait 24 hours, then go on to find their killer. If even a permastrike came of it, roleplaying an assassin might still work. But current server rules effectively (though not explicitly) disallow playing an assassination.
You aren't allowed to assassinate NPC's or PC's without Dungeon Master permission / overview. That's exactly right, but I mention it because the DM overview part is the bit that people must be aware of.No, you are not allowed to assassinate NPC's either. That would require a module change to remove the NPC(s). This is the rules as explained to me by a Dungeon Master, and is no way confrontational. If and of this seems disconcerting, however, that is certainly your viewpoint.
If you are an Assassin a Dungeon Master might well consider it valid roleplay for you to take on an assassination of an NPC, just like for PC player. This isn't far fetched because many adventures end with the assassination of 'bosses' (NPC elites or leaders). An assassination contract isn't any different from a combat adventure in that regard. But you need a Dungeon Master for it.
If the original question was if you can try to assassinate the Dukes of Baldur's Gate, for example, then I imagine you will first have to convince a Dungeon Master that you have an actual roleplay reason to attempt that. (that it's not an out-of-character desire or whim)
During the Amn-Baldur's Gate war of 1349 DR (I think) one of the Amnian commanders was assassinated by a mysterious group of assassins. Its not unprecedented to assassinate NPC's. Its also not unprecedenteed that NPC's may wish to assassinate player characters, like Paladins that have been a thorn in the proverbial backside.

