With Hawaii, we didn't even bother with a referendum; we simply surrounded Queen Liliuokalani's palace with Marines and told her that she wasn't in charge anymore.
The Congress refused to ratify that event.
Eventually, President McKinley did, a few years later.
The Senate refused to ratify the annexation.
During the Spanish American war, a simple majority of both houses voted for annexation.
By the time of annexation, the population of "native" Hawaiians had dwindled to where they were a minority in the Islands.