It would only count if that person did a major portion of damage to the last of their health. So imagine you're shooting at someone, but then they manage to escape cause someone else attacks you. They run up a stairwell and turn the corner where someone else surprises them and gets the kill.
That still leads to problems (like if the other person only does 10% damage but still kills them after you "let them go"). Perhaps make it time based then? Like if you don't shoot them within 5 seconds then they are up for grabs and someone else can then steal the kill? (And if they kill themselves within 5 seconds of being shot it counts as your kill, anything after would count as a -1 suicide).
You could make it so that when someone dies, 10 points are distributed based on damage dealt. You deal 10% of someone's health, you get 1 point. 20, you get 2. 24, you still get 2. 28, you get 3. ect. Hell, it could even go into decimals. Anywhere from 0.1 to 10.0. Then maybe an extra point for being the last one to hit. If the player suicides, they lose points based on the amount of damage they did to themselves. If they took off the last 10 % of their health, they lose a point. They suicide from 100, they lose 10. --- 2% of GameFAQs users have this in their signature. If you're one of the 98% that doesn't, copy and paste this into your signature.