Makos, 13b: It teaches us that just as Avodah Zarah is a warning not to transgress, for which one brings a Korban, so too does one only bring a Korban Chatas for a La'av - where the warning is not to transgress, but not for Pesach and Milah, which are both Mitzvos Asei. ¹

Horayos, 8a #1: It teaches us that, the Par He'elam Davar shel Tzibur, like the Par of Avodah Zarah, is confined to a ruling that entails Zedono Kareis and Shig'gaso Chatas. ²

Horayos, 8a #2: It teaches us that, by Ir ha'Nidachas, although the Torah differentiates between the majority that sinned and a few individuals be'Meizid, ³ by Shogeg, the Din is the same - and they bring a Se'irah as a Chatas.

Kerisos, 2a: It teaches us that a Megadef - someone who curses Hashem be'Shogeg - is neither Chayav a Chatas if he knows he sinned nor an Asham Taluy if he doesn't, ⁴ since, as opposed to Avodah Zarah, he did not perform an act.

Shabbos, 153b: Comparing the whole Torah to Avodas-Kochavim, it teaches us that, like Avodas-Kochavim, one is only Chayav to bring a Chatas if one performs a personal act - to preclude 'Mechamer .. ', someone who leads his donkey on Shabbos. ⁵