<p>I think (and I have nothing to back this up so if someone provides a supported opinion, listen to them) that "prefer not to state" is probably treated as "caucasian" to the adcoms.</p>
<p>"Prefer not to state" won't hurt you, but then again, marking Caucasian technically doesn't hurt you either. It just doesn't give you any preference in admissions - only the Hispanic/African-American/etc. boxes will help.</p>