The Secretary of State of Arizona is not bounded by Hawaiian law. He is bounded by Constitutional law, and Arizona law, provided Arizona law does not conflict with Constitutional law.
If Hawaii (really Obama) refuses to produce the correct documents, then the Secretary has a duty to reject a candidate who has not demonstrated qualifications for office.
He shirked that duty due to unpleasant political pressure.
The Secretary of State in Arizona, and every other state, can only ask the state of a person not born in Arizona to provide confirming information.
There is no state law in any state that requires candidates to present a birth certificate in order to qualify for the state ballot. There was four years between 2008 and 2012 to pass such laws, no state did.
Arizona’s election law requires candidates for president to sign a notarized statement attesting to being “a natural born citizen of the United States.”
That attestation can be challenged in court.
Barack Obama’s statement was challenged and the court ruled that Obama is a natural born citizen. {Allen v. Obama}.