Less than or equal to 0.5%
Initiated automatically

“A recount of the vote is required when the canvass of returns in a primary or general election shows that the margin between the two candidates receiving the greatest number of votes for a particular office, or between the number of votes cast for and against initiated or referred measures or proposals to amend the Constitution of Arizona, is less than or equal to one-half of one percent of the number of votes cast for both such candidates or on such measures or proposals.” A.R.S. § 16-661(A).

“When the court orders a recount of votes which were cast and tabulated on electronic voting equipment, such recount shall be pursuant to section 16-664.  On completion of the recount, and for legislative, statewide and federal candidate races only, the county chairmen of the political parties entitled to continued representation on the ballot or the chairman's designee shall select at random without the use of a computer five per cent of the precincts for the recounted race for a hand count, and if the results of that hand count when compared to the electronic tabulation of that same race are less than the designated margins calculated pursuant to section 16-602, the recount is complete and the electronic tabulation is the official result.  If the hand count results in a difference that is equal to or greater than the designated margin for that race, the procedure established in section 16-602, subsections C, D, E and F applies.” A.R.S. § 16-663(B).

Timing: A.R.S. § 16-663(A).  “The superior court …shall forthwith make and enter an order requiring a recount of the votes….”