When can a police officer ask you to take a sobority test?

A police officer needs only reasonable suspicion of driving while intoxicated to ask you to submit to a sobriety test, actually called an SFST: Standard Field Sobriety Test. You are not obligated to submit to such a test. However, if you do not take the test, the officer will act on the observations he has already made of your behavior, and may arrest you for driving under the influence. He will then ask you to submit to a breath or blood test. If you refuse one of those, you will have your driver's license revoked.