Shevuos, Chapter 2, Mishnah 3. This mishnah deals with the halachos that apply to someone who entered the Azarah of the Beis HaMikdash in a state of purity and then became tamei while inside the Azarah itself.
The wording of the mishnah and its cases:
The mishnah opens: "Nitma ba'azarah" - a person who became tamei while he was in the Azarah. From here the mishnah lists three situations of forgetting:
"V'ne'lam mimenu hatumah v'zachur es hamikdash" - he became tamei and immediately forgot his tumah, but he remembers that he is in the Beis HaMikdash.
"Ne'lam mimenu hamikdash v'zachur es hatumah" - he is aware of his tumah, but he did not realize that he is in the Beis HaMikdash.
"Ne'lam mimenu zeh v'zeh" - he forgot both: that he is in the Mikdash and that he is tamei.
"V'hishtachavah" - this refers to someone who bowed facing inward, with his face directed toward the interior of the Beis HaMikdash, turned inside.
"O sheshahah bichdei hishtachava'ah" - meaning that he lingered for the length of time it takes to bow. This case speaks of someone who bowed while facing outward, where the act of bowing itself is not enough; rather, an amount of time known as "kidei hishtachava'ah" must pass. And its measure is: the length of time it takes a person to say, at a moderate pace, the verse in Divrei HaYamim, "And they bowed with their faces to the ground upon the pavement, and they prostrated themselves and gave thanks to Hashem, for He is good, for His kindness is forever."
It emerges that even if he bowed much more quickly, when he is facing outward he must make sure that the bowing lasts as long as it takes to say this verse. This distinction between one who faces inward and one who faces outward is a halachah handed down to Moshe at Sinai.
"Ba lo ba'arukah" - alternatively, when he leaves the Beis HaMikdash, he takes a route longer than necessary. In this case he is obligated to bring a korban oleh v'yored, exactly like someone who was already tamei and entered the Beis HaMikdash.
"Baketzarah" - but if he left by the shortest possible route, he is exempt. Since he became tamei in the Beis HaMikdash and left as soon as he was able, he is not obligated to bring a korban for having been tamei in the Beis HaMikdash.
"Zu hi mitzvas asei shebamikdash":
The mishnah summarizes and establishes that the obligation to leave the Beis HaMikdash is a positive commandment connected to tumah in the Mikdash. This is not speaking about someone who was tamei and entered the Beis HaMikdash, which is a prohibition, but rather about a case in which a positive commandment rests upon him to leave the Beis HaMikdash.
However, this is a positive commandment in the Mikdash "she'ein chayavin aleha" - for which one does not bring a communal korban. How so? If a beis din were to rule on the laws of leaving the Beis HaMikdash, and erred and instructed that one may even take the long route instead of the short route, this would be an error regarding an obligation of kares. Normally, when a beis din errs regarding an obligation of kares and the majority of Israel acted according to their ruling, they must bring a bull for their forgetfulness and their error in halachah, as explained in Maseches Horayos.
However, the kareis liability incurred by entering the Beis HaMikdash in a state of tumah is not among the transgressions for which this offering is brought, and beis din does not bring a bull for it. The reason: an individual who brings a korban for this transgression brings a korban oleh v'yored, a sliding-scale offering, and not a fixed chatas. The offering varies according to a person's financial means: sometimes an animal, sometimes a bird, and if he cannot afford even that - a meal offering. Since the offering varies and is not a fixed chatas, and beis din brings a korban only for a kareis liability whose offering is a fixed chatas, this is a mitzvah for which beis din does not bring a korban.
In summary: In this Mishnah we learned the law of one who became tamei in the Azarah in three forms of forgetting - he forgot about the tumah, he forgot about the Mikdash, or he forgot about both. If he bowed down facing inward, or lingered facing outward for the measure of time known as 'the time it takes to bow down,' or left by the longer route - he is obligated to bring a korban oleh v'yored; and if he left by the shortest route - he is exempt. The obligation to leave is a positive commandment relating to the Mikdash, and although kareis is involved, beis din does not bring a bull for it, since its offering is a korban oleh v'yored and not a fixed chatas.