  We give the semiclassical asymptotic of barrier-top resonances for
Schr\"{o}dinger operators on ${\mathbb R}^{n}$, $n \geq 1$, whose potential is
$C^{\infty}$ everywhere and analytic at infinity. In the globally analytic
setting, this has already been obtained. Our proof is based on a propagation of
singularities theorem at a hyperbolic fixed point that we establish here. This
last result refines a theorem of the same authors, and its proof follows
another approach.
