  A search for T-violating muon polarization in the $K^+ \to \pi^0 \mu^+\nu$
decay has been performed at KEK using stopped kaons. A new improved limit was
obtained, $P_T= -0.0017 \pm 0.0023 (stat) \pm 0.0011 (syst)$, corresponding to
a 90 % confidence limit of $| P_T| < 0.0050$. The T-violating parameter was
also determined to be Im$\xi = -0.0053 \pm 0.0071 (stat) \pm 0.0036 (syst)$,
and $|{rm Im}\xi| < 0.016$ (90 % CL).
