In the shiur of Chief Rabbi Rav Yitzchak Yosef last night he paskened that there is no need to purchase special cigarettes with a special hechsher for Pesach. Rather, one could buy any cigarette and smoke it on Pesach, even "American cigarettes" - whatever that is.

Rav Yosef mentioned a rav who said that you cannot smoke cigarettes on Pesach because they are all chametz. He attacked him for arguing against something his father, Rav Ovadia, had written and said you don't just start learning halacha at age 50!

Rav Yosef explained that cigarettes are ok because they are not edible for a dog. He did clarify and say that one who does not smoke at all is even better because it is dangerous, but someone who does smoke does not need to look for a KFP hechsher on his cigarettes.
source: Kikar