The four-fermion contact-interaction searches in the process $e^+e^-\to\mu^+\mu^-$ at a future $e^+e^-$ Linear Collider with c.m. energy $\sqrt{s}=0.5$ TeV and with both beams longitudinally polarized are studied. We evaluate the corresponding model-independent constraints on the coupling constants, emphasizing the role of beam polarization, and make a comparison with the case of Bhabha scattering.
