An ab initio molecular orbital study has been carried out for the C2P radical, a molecule which could be of astrophysical interest, on the doublet and quartet surfaces. Geometries have been obtained at the MP2/6-31G* level, whereas MP4 theory has been employed to compute electronic energies. We have found that the CPC isomer lies quite high in energy, but there are two states quite close in energy : linear CCP ((II)-I-2 state) and cyclic C2P (B-2(2) state). We predict linear CCP to be the ground state, but with cyclic C2P lying just about 6 kcal/mol above. These two states are predicted to have high dipole moments, 3.293 and 2.535 D, respectively. Harmonic vibrational frequencies and infrared intensities have also been estimated. In the case of the cation, we have found that linear CCP+ is also the ground state whereas the energy difference with the cyclic C-2 upsilon Symmetric state is now higher than in the case of the neutral system, about 15 kcal/mol.