A continuous coarse-grained potential model for associating fluids, consisting of an off-center specific site bonded with a harmonic potential to a center particle, has been developed and used in canonical molecular dynamics simulations. The thermodynamic, structural, and dynamic properties of the limiting nonassociating reference coarse-grained fluid are investigated as functions of the mass distribution and bond strength between center and site particles. It is theoretically shown and confirmed by simulation that in this limit variations in these potential parameters do not alter the equation of state of the reference coarse-grained fluid but that they have profound influences on both the translational and the rotational dynamics. From the simulation results we arrive at some guidelines that should be kept in mind in the selection of appropriate values for the model parameters. This work provides the precursory knowledge for the study of coarse-grained associating fluids using the conventional molecular dynamics method.