The company said it was co-operating fully with police.
"When one of our guests reported an alleged sexual assault on board Ovation of the Seas we contacted the New Zealand police."
Azzi, a New South Wales demolition worker, was bailed to a New South Wales address but ordered to return to New Zealand for all court hearings.
He was ordered to abstain from alcohol or drugs and has to report to the Merrylands police station three times a week.
Judge Crosbie also said Azzi was not to contact the complainant or four witnesses and was not to leave Australia aside from court appearances.
He is next due in Dunedin District Court in March.
Last month, a 33-year-old man was arrested over another alleged sex attack related to a cruise ship docked in Dunedin.
He was charged with rape and sexual violation by unlawful sexual connection over the alleged December 12 attack.
The defendantis scheduled to appear again next week.