We study the low-energy electronic properties of a junction made of two crossed metallic carbon nanotubes of general chiralities. We derive a tight-binding tunneling matrix element that couples low-energy states on the two tubes, which allows us to calculate the contact conductance of the junction. We find that the intrinsic asymmetries of the junction cause the forward- and backward-hopping probabilities from one tube to another to be different. This defines a zero-field Hall conductance for the junction, which we find to scale inversely with the junction contact conductance. Through a systematic study of the dependence of the junction conductance on different junction parameters, we find that the crossing angle is the dominant factor that determines the magnitude of the conductance.