New Mexico Constitution Art. XIX, § 2. Constitutional convention

Whenever the legislature, by a two-thirds vote of the members elected to each house, deems it necessary to call a convention to revise or amend this constitution, they shall submit the question of calling such convention to the electors at the next general election, and if a majority of all the electors voting on such questions at said election in the state votes in favor of calling a convention, the legislature shall, at the next session, provide by law for calling the same. Such convention shall consist of at least as many delegates as there are members of the house of representatives.

Revisions or amendments proposed by a constitutional convention shall be submitted to the voters of the state at an election held on a date set by the convention. The revisions or amendments proposed by the convention may be submitted in whole or in part, or with alternatives, as determined by the convention. If a majority vote favors a proposal or alternative, it is adopted and becomes effective thirty days after the certification of the election returns unless otherwise provided by the convention.