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 initionine-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.; Bačić, 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 5D 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 Dand 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 Dand Hintermolecular vibrational states in the respective intramolecular manifolds. Comparison is made with the experimental data available in the literature.