We studied the temperature dependence of the specific contact resistance of the copper/GaMnAs interface in the range from 15 K to 290 K. This range includes the Curie temperature of the GaMnAs film of about 145 K. is typically as low as cm, and decreases slowly with decreasing temperature . However, as approaches Curie temperature jumps to about double its value. We suggest that this behavior arises from the suppression of one of the two spin conduction channels, resulting in substantial spin polarization. This might offer a convenient scheme to estimate the spin polarization at a single ferromagnetic/nonferromagnetic interface using all-electrical measurements.