What happens if the Nasi sets aside a female animal for this offering: Temurah 20a
What happens if the Nasi sinned as a normal person, and was then appointed Nasi before bringing the offering: Ketuvot 45a-b
What happens if the Nasi sinned as a normal person, and set aside a male animal at the time [for the sin offering, which was supposed to be female], and then became Nasi and sinned again: Temurah 20a