We proposed the associative memory model with one-to-many associations and analyzed its recall process by the statistical neurodynamics. Since many associative items are recalled simultaneously in the case of one-to-many associations, an external input, which is a cue from a context, must be injected in order to recall one of associative items dynamically. Using the external input, one of associative items can be recalled selectively. We have found that there is a critical loading rate in the present model, above which all equilibrium states are stable, but cannot be reached by the external input. The critical loading rate is defined as the reachable equilibrium states by the external input are disappeared. We will discuss how the critical loading rate depends on the model parameters.