In some states if you refuse a field sobriety test before they arrest you, you could lose your driver’s license, potentially.

But once they’ve arrested you, I don’t know of any state that would require the field sobriety test. Some states would require a regular test which would be done at the station or the hospital. Field sobriety tests are not reliable, so the cops are going to want to do a proper test that is more reliable. But whether these latter tests are required depends on the situation. And it’s possible that the cops will get a court order requiring you to take one anyway, should you refuse.

In other words, field sobriety tests are designed to establish probable cause so that they can arrest you. But they aren’t designed to prove beyond a reasonable doubt that you’re DUI.