The resistance of a heavy metal can be modulated by an adjacent magnetic material through the combined effects of the spin Hall effect, inverse spin Hall effect, and dissipation of the spin accumulation at the interface. This phenomenon is known as the spin Hall magnetoresistance. The dissipation of the spin accumulation can occur via various mechanisms, with spin-transfer torque being the most extensively studied. In this work, we report the observation of spin Hall magnetoresistance at the interface between platinum and an insulating altermagnetic candidate, Ba₂CoGe₂O₇. Our findings reveal that this heterostructure exhibits a relatively large spin Hall magnetoresistance signal, which is anisotropic with respect to the crystal orientation of the current channel. We explore and rule out several potential explanations for this anisotropy and propose that our results may be understood in the context of the anisotropies of the spin current channels across the Pt/altermagnetic Ba₂CoGe₂O₇ interface.