Lightning strikes pose a serious natural threat to carbon fiber reinforced polymers (CFRP). Knowledge of the electrical current distribution is essential for modeling the interaction between CFRP with lightning. The anisotropy of CFRP makes the electrical current tend to concentrate on the surface, having significant influence on the current distribution. The conductivity along the depth direction is studied with pulse generators and a dedicated 4-probe fixture. Non-linear effects were observed not only on 6.4/69 \(\mu\)s lightning pulses, but also on 20/500 ns pulses with much less energy, which implies that the breakdown should be dominated by the electric breakdown mechanism. The electric breakdown process is fast, with voltage spikes observed in the leading edge for a few nanoseconds. After the spikes, the transient resistance remains almost constant. Similarities could be found with the phenomena involved in thin polymer film breakdowns.