We describe an experimental test of local realistic and nonlocal realistic theories using polarizationentangled two-photon singlet states created using a fiber-based polarization Sagnac interferometer. We show a violation of Bell s inequality in the Clauser-Horne-Shimony-Holt form by 15 standard deviations, thus excluding local hidden-variable theories, and a violation of a Leggett-type nonlocal hidden-variable inequality by more than three standard deviations, thus excluding a class of nonlocal hidden-variable theories.