Horayot, Chapter Three, Mishnah Two
Mishnah two teaches the halakhah regarding a high priest or king who issue an errant ruling after having relinquished their office.
If the anointed priest relinquished his high priesthood and afterwards transgressed, and similarly if a ruler relinquished his reign and afterwards transgressed, the anointed priest brings a bull while the ruler is like a regular person.
When the high priest is removed from office, he does not lose his sacred status (we will discuss this below in mishnah four). Therefore, even if he issues an errant ruling after having been removed, he is still considered like a high priest, and he brings a bull. However, the king does lose his status, and is therefore treated like a regular person who unwittingly sins and brings a she-goat or female sheep.