  We analyse the sensitivity to physics beyond the SM of T-odd correlations in
$K_{\ell 4}$ decays, which do not involve the lepton polarization. We show that
a combined analysis of $K^+_{\mu 4}$ and $K^-_{\mu 4}$ decays can lead to new
constraints about CP violation in $\Delta S=1$ charged-current interactions,
complementary to those obtained from the transverse muon polarization in
$K_{\mu 3}$ and of comparable accuracy.
