Subsequent to our spectroscopic detection of the C(2)X(X=P,As) free radicals [F. X. Sunahori et al., J. Am. Chem. Soc. 129, 9600 (2007)], we have studied the electronic spectrum of the (2)Delta(i)-X (2)Pi(r) system of the jet-cooled C(2)P free radical in the 490-630 nm region. The high-resolution laser-induced fluorescence spectrum of the two spin components of the 0(0) (0) band of (12)C(2)P has been recorded, and the rotational and spin-orbit coupling constants have been determined for both electronic states. The Renner-Teller effect has been observed in both the (2)Pi and the (2)Delta states, and the vibrational structure has been assigned. For the ground state, all of the observed levels up to 3500 cm(-1) were fitted with a standard Renner-Teller model. The excited (2)Delta state vibrational levels were successfully fitted using literature energy level expressions derived from perturbation theory, yielding vibrational and Renner-Teller parameters for both (12)C(2)P and (13)C(2)P. The molecular structure of C(2)P in the ground and excited states has also been estimated and compared to ab initio calculations and the geometries of similar molecules.