  The rare decay $B\to K^\ast( \to K\pi) \nu\bar{\nu}$ is expected to play an
important role in searches for physics beyond the Standard Model at the near
future $B$-physics experiments. We investigate resonant and non-resonant
backgrounds that arise beyond the narrow-width approximation for the $K^\ast$.
Non-resonant $B\to K\pi \nu\bar{\nu}$ decays are analyzed in the region of low
hadronic recoil, where $B \to K \pi$ form factors from
Heavy-Hadron-Chiral-Perturbation Theory are available. In a Breit-Wigner-type
model interference-induced effects in the $K^*$ signal region are found to be
sizable, as large as $20\%$ in the branching ratio. Corresponding effects in
the longitudinal polarization fraction $F_L$ are smaller, at most around few
\%. Effects of the broad scalar states $K_0^\ast$ and $\kappa$ are at the level
of percent in the branching fraction in the $K^\ast$ signal region and
negligible in $F_L$. Since the backgrounds to $F_L$ are small this observable
constitutes a useful probe of form factors calculations, or alternatively, of
right-handed currents in the entire $q^2$-region. The forward-backward
asymmetry in the $K \pi$-system, $A_{\rm FB \, L}^K$, with normalization to the
longitudinal decay rate probes predominantly S,P-wave interference free of
short-distance coefficients and can therefore be used to control the resonant
and non-resonant backgrounds.
