We report full-dimensional and fully coupled quantum bound-state calculations of the J = 0, 1 intra- and intermolecular rovibrational states of the isotopically asymmetric HDO-CO complex. They are performed on the ab initio nine-dimensional (9D) potential energy surface (PES) [Liu, Y.; Li, J. Phys. Chem. Chem. Phys. 2019, 21, 24101]. The present study complements our earlier theoretical investigation of the 9D rovibrational level structure of the H2O-CO and D2O-CO complexes [Felker, P. M.; Bacic, Z. J. Chem. Phys. 2020, 153, 074107]. What distinguishes HDO-CO is that, unlike the two isotopically symmetric isotopologues, it does not display hydrogen-interchange tunneling but has two distinct isomers, the lower-energy D-bonded HOD-CO and the higher-energy H-bonded DOH-CO. The highly efficient methodology employed in the present calculations derives from our earlier study referenced above, taking into account the lower symmetry of HDO-CO. The full 9D rovibrational Hamiltonian is partitioned into three reduced-dimension Hamiltonians: the SD rigid-monomer intermolecular vibrational Hamiltonian and two intramolecular vibrational Hamiltonians, one for the HDO monomer (3D) and another for the CO monomer (1D), and a 9D remainder term. The reduced-dimension Hamiltonians are diagonalized separately, and small portions of their low-energy eigenstates are incorporated in the compact final 9D product contracted basis covering all internal, intra- and intermolecular degrees of freedom of the complex. The 9D rovibrational Hamiltonian is diagonalized in this fully contracted basis. The calculations show that the eigenstates belonging to the D-bonded and H-bonded isomers, designated as D and H, respectively, are easy to identify, owing to the near-complete localization of their wave functions in either of the two minima on the PES. The computed intramolecular vibrational frequencies of the two monomers are either blue- or red-shifted, depending on the mode. The excitations of the intramolecular vibrational modes affect the energies of the low-lying D and H intermolecular vibrational states in the respective intramolecular manifolds. Comparison is made with the experimental data available in the literature.