The latest style rulings from The Associated Press touch on the sensitive topics of race and ethnicity. Here they are:
A person of Asian birth or descent who lives in the U.S. When possible, refer to a person's country of origin. For example: Filipino-American or Indian-American. Follow the person's preference.
Sometimes used by Mexican-Americans in the Southwest. Not interchangeable with Mexican-American. Use only if a person's preference.
Often the preferred term for a person from — or whose ancestors were from — a Spanish-speaking land or culture or from Latin America. Latina is the feminine form. Follow the person's preference. Use a more specific identification when possible, such as Cuban, Puerto Rican, Brazilian or Mexican-American. See Hispanic, nationalities and races, and race entries.
I like how AP advises specificity. It's more precise and detailed to write and edit in that way. Those details are sometimes hard to get, however.