A study of the resistive and low-temperature magnetoresistive properties of pressed powders of ferromagnetic half-metal chromium dioxide CrO₂ with nanoparticle shape anisotropy. The effects of Fe impurities on the tunneling resistance and magnetoresistance of CrO₂ powders are investigated. It is found that the Fe impurity leads to a decrease in the resistance and tunneling magnetoresistance of chromium dioxide. It is suggested that the decrease in magnetoresistance of the solid solution Cr_1-xFe_xO₂ is associated with the formation of additional localized states at the iron impurities in a tunnel barrier. The influence of the magnetic field input rate on the form of the low-temperature tunneling magnetoresistance hysteresis in Cr_1-xFe_xO₂ powder is considered. It is shown that the low-temperature singularities of magnetoresistance hysteresis depend on the relaxation rate of the magnetic moments of the nanoparticles to the equilibrium state. Possible reasons for such a dependence are discussed.