I have a question on how some AZ elections work........

[Upthevibe]

If a Senator or Congressman in Arizona leaves before their term is up, is there a special election or is the governor able to appoint someone?

Thank you!

[Kali]

1. do you mean US senator/congress? from AZ statutes -

https://www.azleg.gov/ars/16/00222.htm

16-222. Vacancy in the office of United States senator or representative

A. When a vacancy occurs in the office of United States senator or representative in Congress by reason of death or resignation, or from any other cause and except as provided in subsection D of this section, the vacancy shall be filled at the next general election. At such an election the person elected shall fill the unexpired term of the vacated office.

B. For a vacancy in the office of representative in Congress, if the next general election is not to be held within six months after the date of the occurrence of the vacancy, the governor shall call a special primary election and a special general election to fill the vacancy. The governor shall call the special primary election and establish its date within seventy-two hours after the office is officially declared vacant. Notwithstanding sections 16-313, 16-351 and 16-542, for a candidate for office at an election held pursuant to this subsection, the following apply:

1. The special primary election shall be held not less than one hundred twenty nor more than one hundred thirty-three days after the occurrence of the vacancy, and the special general election shall be held not less than seventy nor more than eighty days after the special primary election.

2. Nomination papers and nomination petitions shall be filed not later than thirty days after the date of the proclamation calling the election.

3. Any court action challenging the nomination of a candidate shall be filed not later than 5:00 p.m. on the fifth business day after the last day for filing nomination papers and petitions.

4. The superior court shall hear and render a decision within five days after the filing of the action.

5. Beginning fifteen days before the date of the election, the county recorder or other officer in charge of elections shall mail early ballots within forty-eight hours after receipt of a complete and correct early ballot request from persons qualified to vote.

C. For a vacancy in the office of United States senator, the governor shall appoint a person to fill the vacancy. That appointee shall be of the same political party as the person vacating the office and, except as provided in subsection D of this section, shall serve until the person elected at the next general election is qualified and assumes office. If the person vacating the office changed political party affiliation after taking office, the person who is appointed to fill the vacancy shall be of the same political party that the vacating officeholder was when the vacating officeholder was elected or appointed to that office.

D. If a vacancy in the office of United States senator occurs more than one hundred fifty days before the next regular primary election date, the person who is appointed pursuant to subsection C of this section shall continue to serve until the vacancy is filled at the next general election. If a vacancy in the office of United States senator occurs one hundred fifty days or less before the next regular primary election date, the person who is appointed shall serve until the vacancy is filled at the second regular general election held after the vacancy occurs, and the person elected shall fill the remaining unexpired term of the vacated office.

E. For a vacancy in the office of representative in Congress that occurs simultaneously with at least one hundred additional vacancies in the office of representative in Congress as prescribed by 2 United States Code section 8, a special general election to fill the vacancy in this state shall be held not more than forty-nine days after the declaration of the vacancy unless a regularly scheduled general election or previously scheduled special general election is held within seventy-five days after the declaration of the vacancy.

[Kali]

2. for the state legislature

https://ballotpedia.org/How_vacancies_are_filled_in_state_legislatures#Arizona

If there is a vacancy in the Arizona State Legislature, the board of county supervisors must select a replacement. The secretary of state is required to contact the state party chairperson to give notice of the vacancy. The state chairperson must give notice of a meeting to fill the seat within three business days of receiving notice.[4] The political party committee is involved in the appointment process only if the legislative district has thirty or more elected precinct committeemen.[4]

If the legislative district has 30 or more elected precinct committeemen:

The precinct committeemen must nominate three qualified electors as replacements. If the Legislature is in session, this must occur within five days. If the Legislature is out of session, the committeemen have 21 days to nominate potential replacements. Each elector must receive a majority of the committeemen's vote to earn a nomination. The chair then forwards the three nominees to the board of supervisors. The board of supervisors appoints a nominee from the three names. If the committeemen do not submit a list of names within the allotted timeframe, the board of supervisors proceeds with the vacancy as if the district had fewer than 30 elected precinct committeemen.[4]

If the legislative district has fewer than 30 elected precinct committeemen:

The board of supervisors appoints a panel of citizen supervisors within seven business days of a vacancy occurring. The citizen panel must submit the name of three qualified electors of the same political party as the previous incumbent to the board of supervisors. If the Legislature is in session, this must occur within five days. If the Legislature is out of session, the committeemen have 21 days to nominate potential replacements. The board of supervisors must select a replacement by a majority vote.[5]
The person selected to fill the seat serves the remainder of the unfilled term.[5]

DocumentIcon.jpg See sources: Arizona Rev. Stat. Ann. §41-1202

[dobleremolque]

3. US Constitution sets that

process. If the vacancy is in the house, there is a by-election. If the vacancy is in the senate, 45 states allow the governor to appoint a replacement who serves until the next full election. There are caveats about when the senate vacancy actually occurs. See the 17th Amendment. There's nothing in the Constitution that says the Senate appointee has to be the same political party, although some states are now requiring that via legislative action.
House, see Art 1, Sec 2, Clause 4
Senate, see 17th Amendment.

(See Kali's excellent post above, for probably more than you want to know.)