We continue a dominant WKB solution of the Schr\"odinger equation in the classically forbidden region to an outgoing WKB solution in the classically allowed region across a simple (multi-dimensional) turning point, without assuming the analyticity for the potential. This report explains briefly the method used in \cite{bfm}, where we computed the semiclassical asymptotics of the width of shape resonances for non-globally analytic potentials
