  The work presents the studies of the polarization observables in the single
pion production (SPP) induced by the interaction of the muon neutrino
(antineutrino) with nucleons. The SPP cross-sections and spin asymmetries are
computed within two phenomenological models. One is basing on the nonlinear
sigma model \cite{Hernandez:2007qq}; the other has origin in linear sigma
model~\cite{Fogli:1979cz}. Firstly, we show that the final nucleon polarization
and target spin asymmetries are good observables to obtain information about
the $C_5^A$ axial form factor. Secondly, we demonstrate that the nucleon
polarization and the target spin asymmetries are sensitive to the relative
phase between resonance and nonresonance amplitudes. We conclude that the
polarization of the final nucleon and the target spin asymmetry are promising
observables for testing SPP models, including studies of the axial content of
$\Delta(1232)$ resonance and unitarization procedures.
