We have performed three-degree-of-freedom quantum calculations of HOCO resonances by using a complex potential method. The coordinates we consider are the OH internuclear distance, the CO internuclear distance, and the distance between the centers of mass of the OH and CO fragments. The reduced dimensionality potential has been constructed by adding the nonreactive "spectator" CO coordinate to the previous two-degree-of-freedom potential of Schatz and Dyck [G. C. Schatz and J. Dyck, Chem. Phys. Lett. 188, 11 (1992)] using a Shepard-type interpolation procedure. The positions and lifetimes of more than two hundred resonances are calculated and approximate quantum numbers are assigned. The results are compared with previous two-degree-of-freedom calculations where the GO-stretch mode has not been considered. The appearance of a new group of narrow resonances with a significant CO stretch contribution is reported. The results are tested against the vibrational shifting approximation in which the spectator CO mode is treated adiabatically. The latter is shown to be insufficient for quantitative predictions of resonance positions and widths, however averaged positions and widths are reasonably well described. The rotational shifting approximation is tested by performing the adiabatic rotation calculations of resonances for J=1, K=0 and J=1, K=1 cases, where J is the total angular momentum and K is the body-fixed projection quantum number of a symmetric top. Rotational shifting is shown to work better for K=0 case than for K=1 case.