Whether a Nasi may forgive his honor: Kiddushin 32b
Whether all people must stand before a Nasi, and sit when told to: Moed Katan 27b
At what distance one is supposed to rise for the Nasi: Kiddushin 33b Mourners and Sick People don't stand before a Nasi, but if they stand then the Nasi may not tell them to sit: Moed Katan 27b
No two Leaders may overlap: Moed Katan 28a
Other laws of a Nasi
The Nasi has the same status as a Melech [king]: Rashi Keritot 26a "Mah l'Nasi"
The Nasi does not testify in court: Keritot 26a
Whether a Nasi brings a sliding-scale korban as others do for certain sins, or whether he brings a different korban: Keritot 2b