  We analyze theoretically the $D^+\to \nu e^+ \rho \bar K$ and $D^+\to \nu e^+
\bar K^* \pi$ decays to see the feasibility to check the double pole nature of
the axial-vector resonance $K_1(1270)$ predicted by the unitary extensions of
chiral perturbation theory (UChPT). Indeed, within UChPT the $K_1(1270)$ is
dynamically generated from the interaction of a vector and a pseudoscalar
meson, and two poles are obtained for the quantum numbers of this resonance.
The lower mass pole couples dominantly to $K^*\pi$ and the higher mass pole to
$\rho K$, therefore we can expect that different reactions weighing differently
these channels in the production mechanisms enhance one or the other pole. We
show that the different final $VP$ channels in $D^+\to \nu e^+ V P$ weigh
differently both poles, and this is reflected in the shape of the final
vector-pseudoscalar invariant mass distributions. Therefore, we conclude that
these decays are suitable to distinguish experimentally the predicted double
pole of the $K_1(1270)$ resonance.
