The rule of asham taluy appears in the Torah (Vayikra 5:17-19), and its rules are discussed in detail mainly in Massekhet Keritot. The Torah does not specify what transgression would obligate this sacrifice to be brought; nevertheless, there is a long-standing Rabbinic tradition which teaches that an asham taluy was brought when a person accidentally performed an act that may have been forbidden by the Torah – one for which he would have been obligated to bring a korban hatat (a sin offering) had we known for sure that the act was prohibited. In such a case, the person would bring the asham taluy, and if it later became clear that he had, in fact, transgressed, the sinner would bring an additional korban hatat at that time.
The tanna’im differ as to the level of uncertainty that obligates a person in an asham taluy, but the conclusion is that the sacrifice is brought only in the case of hatikha ahat mi-shtei hatikhot – “one piece out of two.” This means that an asham taluy is only brought when the question is whether an act which is forbidden was done. If, however, there is a question with regard to the act itself, i.e. we are not certain whether the act was forbidden at all, then an asham taluy would not be brought. The specific example given is a case where a person had two pieces of meat in front of him: one was permitted and one was forbidden; we are certain that he ate one piece, but we are unsure which piece it was. Another such case would be if we knew for certain that the piece was forbidden, but we are uncertain as to whether the person ate the minimum amount necessary to be obligated in a sin-offering. In these two cases, an asham taluy would be required. If, however, we are not sure whether the piece that was eaten was truly forbidden – it was a case of hatikha ahat, “a single piece” – then an asham taluy would not be brought.