During the last 4 years we have monitored the optical radial velocities of 34 optically bright carbon stars in the solar neighborhood. We compare these measurements with the velocities of circumstellar CO radio emission lines taken from the literature. Twelve stars of the 34 show a large offset, greater than 5 km s-1, between the CO and optical velocities. This group distinguishes itself by several characteristics: (1) IRAS and 2-mu-m colors, (2) variability class (most arc Miras), (3) large amplitude of optical velocity variation over several epochs, (4) strong H-alpha emission, and (5) relatively large mean outflow velocity of the circumstellar matter. The optical velocities for this group are consistently redshifted from the CO mean, whereas the optical velocities for the other carbon stars are distributed on either side of their mean CO velocity. This redshift bias in optical velocity might be related to the shock structure or pulsational mode of these stars. In addition, we report a mean amplitude of optical velocity variation of 8.0 km s-1 and 2.4 km s-1 for the Mira and SR variables, respectively. CO velocities can, in principle, provide a good measure of the center-of-mass motion, and although there are differences in some reported CO velocities which are outside the quoted errors, most are consistent to within 1 km s-1.