To address recent electron panmagnetic resonance experiments showing a distortion at the H2-site lowering the defect symmetry from cubic to tetragonal in CaO crystal, we have investigated the defect-induced lattice relaxation of an H2ion in CaO with local Oh and D4h symmetry respectively using a first-principles embedded-cluster approach based on the local density approximation of dcnsity functional theory. We show that the ground State in oh symmetry is an~orbitally degenerate tlu state, while in D A ~ symmetry it is an a, state. This Jahn-Teller distortion of the Ca0H'-system is consistent with the experimental findings. We find th3t the position of the HOMO tlu root in the bandgap is sensitive to the inclusion of the 3d orbital at the nearest-neighbour Caz' sites suggesting a bonding interaction. The Fermi contact spin density at the proton is in good agreement with the observed values, while a significant discrepancy is found at the Ca2+ sites. Mulliken analysis indicates that the spin density at the proton is mainly due to the care polarization of the Hz-Is orbital.