The rate of inelastic nuclear interactions in a short bent silicon crystal was precisely measured for the first time using a 180 GeV/c positive hadron beam produced in the North Experimental Area of the CERN SPS. An angular asymmetry dependence on the crystal orientation in the vicinity of the planar channeling minimum has been observed. For the inspected crystal, this probability is about ∼ 20% larger than in the amorphous case because of the atomic density increase along the particle trajectories in the angular range of volume reflection, whose dimension is determined by the crystal bending angle. Instead, for the opposite angular orientation with respect to the planar channeling, there is a smaller probability excess of ∼ 4%.