Issues in relation to which referendums are mandatory at the national level

The Constitution of the Cook Islands is at: http://www.parliament.gov.ck/Constitution.pdf

Certain constitutional amendments (altering 4 year parliamentary terms or Head of State).  See sections 37(7) and 41(2) of the Constitution of the Cook Islands.

Otherwise, the Constitution of the Cook Islands is amendable by ordinary Act of its Parliament, as is the case in the Westminster systems of the UK and New Zealand, from which the Cook Islands gained independence in 1965:  see section 41 and the First and Second Schedule to the Constitution.