The ship's owner Carnival is under investigation in Australia after hundreds of passengers were infected with the virus.
The Ruby Princess visited New Zealand from 11-15 March, docking in Milford Sound, Dunedin, Akaroa, Wellington and Napier before returning to Sydney.
After the Australian investigation was announced earlier this month, Prime Minister Jacinda Ardern asked Crown Law to investigate and Attorney-General David Parker has received legal advice.
New Zealand agencies are now engaging with Australian authorities and sharing information with them, says Customs Investigations Manager Bruce Berry.
"Our investigation seeks to establish whether any offences have been committed, including against the Customs and Excise Act 2018, specifically whether the cruise ship made the appropriate declarations prior to arrival and receiving clearance to enter New Zealand."
Offences against the Customs and Excise Act 2018 can carry a term of imprisonment or a fine, including against a body corporate.
Customs was liaising with the Ministry of Health, Crown Law and Australian authorities.
"We are unable to comment further at this time, due to the ongoing investigation both here in New Zealand and in Australia."