We report the effects of etch process parameters on the ohmic contact formation in the plasma etching of GaN. Planar inductively coupled plasma system with $CH_4/H_2/Ar$gas chemistry has been used as etch reactor. The contact resistance and the specific contact resistance have been investigated using transfer length method as a function of RF bias power and %Ar gas concentration in total flow rate. AES(Auger electron spectroscopy) analysis revealed that the etched GaN has nonstoichiometric Ga rich surface and was contaminated by carbon and oxygen. Especially large amount of carbon was detected at the sample etched for high bias power (or voltage) condition, where severe degradation of contact resistance was occurred. We achieved the low ohmic contact of $2.4{ imes}10^{-3} {Omega}cm^2$ specific contact resistance at the input power 400 W, RF bias power 150 W, and working pressure 10mTorr with 10 sccm $CH_4$, 15 sccm H2, 5 sccm Ar gas composition.