The geometry and vibrational frequencies of the ozone molecule are studied using the reduced multireference coupled cluster method with singles and doubles (RMR CCSD) relying on a two-electron/two-orbital (2, 2) active space. The role played by the choice of the reference space is analyzed in detail by considering both the spin adapted, two-configuration reference space and the complete three-configuration reference space based on the (2, 2) active space. It is shown that while the two-reference RMR CCSD approach, using the C-2 upsilon symmetry-adapted (2,2) active space, provides a better description of the geometry and harmonic frequencies of symmetric vibrational modes than the standard single-reference (SR) CCSD method, the three-reference approach is essential to achieve an accurate description of the harmonic frequency of the asymmetric stretching mode. A unique behavior of ozone in this regard is highlighted by a comparison with other symmetric triatomics. The comparison with results obtained by other methods, including the SR configuration interaction with singles and doubles (CISD), the standard SR CCSD, as well as two-reference and large reference space MR CISD methods, clearly demonstrates the superiority of the RMR CCSD approach. In fact, the performance of a small reference space RMR CCSD method is similar to that of a large reference space MR CISD, thus enabling a compact description of both dynamical and nondynamical correlation effects in states having a multireference character.