  We establish propagation of singularities for the semiclassical Schr\"odinger
equation, where the potential is conormal to a hypersurface. We show that
semiclassical wavefront set propagates along generalized broken
bicharacteristics, hence reflection of singularities may occur along
trajectories reaching the hypersurface transversely. The reflected wavefront
set is weaker, however, by a power of $h$ that depends on the regularity of the
potential. We also show that for sufficiently regular potentials, wavefront set
may not stick to the hypersurface, but rather detaches from it at points of
tangency to travel along ordinary bicharacteristics.
