The transverse acoustic impedance of superfluid ^{3}He was measured in the A1 and A2 phases up to 13 T to investigate the surface states in nonunitary superfluids. The temperature dependence of the impedance was much larger in the A1 phase than in the A2 phase. This nonsymmetric behavior indicates that momentum exchange with walls for spin-down surface states is quite different from that for spin-up surface states. The spin-dependent response might be a reflection of an essential feature of the nonunitary states where gap amplitudes depend on spin states. Weak-coupling theories ignore any spin-dependent processes and do not account for the nonsymmetric behavior.