Ariz. Rev. Stat. § 41-1202
A. If a vacancy occurs or exists in the legislature and the vacant seat was represented by a political party that is organized pursuant to title 16, chapter 5, article 2 and that has at least thirty elected committeemen who are from precincts that are in the legislative district and that are in the county in which the vacancy occurred, the following apply:
4. The meeting to select nominees to fill the vacancy is subject to title 38, chapter 3, article 3.1, and the state party chairman of the appropriate political party shall oversee the nominations. Fifty percent or more of the elected precinct committeemen of the district who are in the legislative district and from the county in which the vacancy occurred, or their proxies, meeting together constitutes a quorum for the purposes of this subsection. A precinct committeeman may choose to allow the use of a proxy that:
B. If a vacancy occurs in the legislature and the vacant seat was represented by a political party that is organized pursuant to title 16, chapter 5, article 2 and that has fewer than thirty elected committeemen who are from precincts that are in the legislative district and that are in the county in which the vacancy occurred or if the vacant seat was not represented by a political party that is organized pursuant to title 16, chapter 5, article 2, the following apply: