  We calculate at the leading order in $\alpha_s$ the QCD amplitude for
exclusive neutrino production of a $D^*$ or $D_s^*$ charmed vector meson on a
nucleon. We work in the framework of the collinear QCD approach where
generalized parton distributions (GPDs) factorize from perturbatively
calculable coefficient functions. We include $O(m_c)$ terms in the coefficient
functions and $O(m_D)$ term in the definition of heavy meson distribution
amplitudes. The show that the analysis of the angular distribution of the decay
$D_{(s)}^*\to D_{(s)} \pi$ allows to access the transversity gluon GPDs.
