From the PFSRD for the Oathbow magic item:
Of elven make, this white +2 composite longbow (+2 Str bonus) whispers “Swift defeat to my enemies” in Elven when nocked and pulled. Once per day, if the archer swears aloud to slay her target (a free action), the bow's whisper becomes the shout “Death to those who have wronged me!” Against such a sworn enemy, the bow has a +5 enhancement bonus, and arrows launched from it deal an additional 2d6 points of damage (and ×4 on a critical hit instead of the normal ×3). After an enemy has been sworn, the bow is treated as only a masterwork weapon against all foes other than the sworn enemy, and the archer takes a –1 penalty on attack rolls with any weapon other than the oathbow. These bonuses and penalties last for 7 days or until the sworn enemy is slain or destroyed by the wielder of the oathbow, whichever comes first.
The oathbow may only have one sworn enemy at a time. Once the wielder swears to slay a target, he cannot make a new oath until he has slain that target or 7 days have passed. Even if the wielder slays the sworn enemy on the same day that he makes the oath, he cannot activate the oathbow's special power again until 24 hours have passed from the time he made the oath.
This makes it pretty specific that the oathbow wielder has to be the one to slay the target, or suffer the penalties for a week. If you are up against a single opponent in melee, and someone else in the party slays your sworn target, do you suffer penalties for a week until you can reswear against something else?