The star candle firework is a type of firework that can be used as a ranged weapon, dealing 1 nonlethal damage and 1 fire damage.
Unlike most alchemical weapons, this one can actually be used for sneak attacks, requiring an attack roll and not being a splash weapon. The difficult part is determining what type of damage is dealt by the sneak attack: nonlethal, fire, or a mix of the two?
The Sneak Attack ability says that:
With a weapon that deals nonlethal damage (like a sap, whip, or an unarmed strike), a rogue can make a sneak attack that deals nonlethal damage instead of lethal damage.
The Star Candle Firework fires a number of projectiles which each
deal 1 point of nonlethal damage and 1 point of fire damage if they hit
I cannot think of another non-technological weapon, other than a torch that inherently does elemental damage without being enchanted.
I would read the Firework's fire damage similarly to the torch, that it does "one point of nonlethal damage, plus one point of fire damage"; much like, say, a Flaming sword that deals an additional 1d6 fire, the fire is over and above whatever would normally happen.
Therefore, sneak attacking with the firework* would deal additional nonlethal damage. Note that the firework's description fails to mention the type of nonlethal damage it does (B/S/P).
*which sounds awesome, by the way
The rules for the star candle are deficient; there is no such thing as “nonlethal” damage. Nonlethal is an optional modifier on your damage, but damage still needs a type. Is this nonlethal piercing damage? Nonlethal bludgeoning damage? No one knows, because it doesn’t say.
Moreover, weapons do not deal mixed-physical-and-energy damage as their base damage. The closest comparison is the torch, which deals damage as a gauntlet of its size, “plus 1 point of fire damage.” The use of “plus” there indicates (to me, anyway, though it could be clearer) that the fire damage is bonus damage, and so the extra damage added by sneak attack with a torch would be bludgeoning (as with a gauntlet), still with just the +1 fire damage.
But the star candle claims to deal “1 point of nonlethal damage and 1 point of fire damage.” The “and” term when used for weapon damage typically refers to a hybrid type of damage, e.g. “bludgeoning-and-piercing” (e.g. a morningstar), “piercing-and-slashing” (e.g. a hurlbat), “slashing-and-bludgeoning” (e.g. a claw), or “bludgeoning-and-piercing-and-slashing” (e.g. a bite). There is no such thing as hybrid energy damage, however, and hybrid damage does not get specifically broken down (e.g. if a morningstar rolls an 8 on its damage, it deals 8 bludgeoning-and-piercing damage, not 4 bludgeoning and 4 piercing).
So despite using “and,” the star candle rules cannot possibly mean that it deals hybrid damage. Instead, it seems to be implying that one or the other is a bonus, or that this is some new, unique case where a weapon has two distinct types of non-hybrid damage in its base damage. Either way, we have a problem: if it’s the former, we don’t really know which is the base and which is the bonus, and if it’s the latter, we have no rules for that.
The most sane thing to do with it is to treat the “nonlethal” damage, after you have decided what damage type it should actually have, as the base, and the fire damage as the bonus. Then the sneak attack damage would be the same damage type as the nonlethal damage (and, presumably, it would stay nonlethal with sneak attack, as the damage of a sap does).
Well, actually, the most sane thing to do is to throw out this not-even-completely-thought-through piece of garbage. It adds nothing to the game. If you like the idea (which is a fine thing), just write your own firework alchemical weapon from scratch; you don’t need or want Paizo’s shoddy work in this regard.
