Pesachim, Chapter 7, Mishnah 8. The Mishnah deals with the law of a Pesach offering that became tamei, and distinguishes between tumah that affected most of the offering and tumah that affected only a small part of it - both regarding the place where it is burned and regarding the wood used to burn it.
"Nitma shalem o rubo":
The Mishnah opens: "Nitma shalem o rubo - sorfin oso lifnei ha'birah" - if the entire Pesach offering became tamei, or if most of it became tamei, it is burned before the birah. This refers to a case where the offering was already brought and its blood was sprinkled, but there was not yet time to eat it; and likewise even if a small amount of it was already eaten, provided that most of it became tamei.
What is "the birah":
Rabbi Yochanan and Reish Lakish disagree about this in the Gemara in Maseches Yoma:
Rabbi Yochanan: a particular place on the Temple Mount.
Reish Lakish: the entire Beis HaMikdash.
In either case, the burning is done in a public place, and the reason is this: the Sages decreed that it be done publicly in order to embarrass the owners, so that they will be more careful in the future not to allow the Pesach offering to become tamei. For this reason, this halachah applies specifically when the entire offering, or most of it, became tamei.
And when it is burned before the birah, one is permitted to use "me'atzei ha'ma'arachah" - the communal wood ordinarily designated for the arrangement of wood on the Altar.
"Nitma mi'uto o ha'nosar":
If only a small part of the Pesach offering became tamei, or if some of it remained as nosar that there was no time to eat - "sorfin oso b'chatzroseihen o al gagoseihen me'atzei atzman" - it is burned in the courtyards of their houses or on their roofs, within Yerushalayim, and with their own wood. Only in the Mikdash may one use the communal wood.
"Ha'tzikanin":
The Mishnah concludes: "Ha'tzikanin sorfin oso lifnei ha'birah, bishvil lehanos me'atzei ha'ma'arachah" - the tzikanin are the misers, and they are permitted to bring their nosar, or the small part that became tamei, to the Beis HaMikdash and burn it before the birah, so that they too may benefit from the communal wood and save on their expenses.
In summary: in this Mishnah we learned that when an entire Pesach offering, or most of it, became tamei, the burning is done before the birah, in public, because of the law of embarrassing the owners, and with the wood of the ma'arachah; whereas when only a small part became tamei, or in the case of nosar, it is burned in the courtyards and on the roofs of Yerushalayim and with one's own wood. We also learned of the leniency granted to the tzikanin to burn before the birah in order to benefit from the wood of the ma'arachah.