Resistive, magnetoresistive, and magnetic properties of chromium dioxide CrO₂ nanopowders were studied. The powders consisted of either spherical or needle-shaped nanoparticles that were covered with dielectric shells of varying composition and thickness. Anisotropy of the tunnel magnetoresistance for all the powders was found. It was shown that the anisotropy of the tunnel magnetoresistance of CrO₂ powders is associated with the formation of an induced magnetic texture, and is determined by the difference in the sample magnetization rate along and perpendicular to the plane of pressing of powders.