Per the Arizona Constitution, calling a special session requires a 2/3 majority vote in both houses of the legislature. The state Constitution is the final authority in the matter. The U.S Constitution gives the legislatures the power to select electors, but they still have to follow the rules set out in the state Constitution.
“(2) Upon the presentation to the governor of a petition bearing the signatures of not less than two-thirds of the members of each house, requesting a special session of the
legislature and designating the date of convening, the governor shall promptly call a special session to assemble on the date specified. At a special session so called the
subjects which may be considered by the legislature shall not be limited.”
Ducey can call one, but it’s pretty clear that he won’t.
A state Constitution cannot take the US Constitutional powers away from the state legislatures.
Ever hear of the Supremacy Clause? If the legislature has the sole power to choose electors, that power would appear to supersede the state constitution, which limits such power and gives the governor a veto over that power.