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Anderson arrived in the country on Monday to film a commercial, and is thought to have spent her time in Auckland.
The Hollywood star has teamed up with animal rights group People for the Ethical Treatment of Animals (PETA), which said her arrival in New Zealand had sparked her to write a letter to China Southern Airlines about its practice of shipping primates to overseas research laboratories.
"You may not be aware that after being torn from the wild or rounded up at dreadful breeding farms, the monkeys you ship from China to laboratories in the US and elsewhere end up imprisoned in tiny, desolate laboratory cages, where they are cut open, addicted to drugs, infected with debilitating diseases, intentionally poisoned, and crippled in cruel experiments," Anderson wrote.
"I ... urge you to have a heart for animals this Valentine's Day and stop shipping monkeys to their deaths in laboratories."
She said she would avoid flying on the airline until it stopped the practice, and she encouraged her friends, family and fans to do the same.
PETA spokeswoman Ashley Fruno said Anderson had been "very hush" about what she was doing in New Zealand and hadn't wanted any attention.
She departs today.
China Southern Airlines could not be reached to comment last night.