We propose a scheme to search for the electrical dipole moments (EDMs) and chromodipole moments (CDMs) of a charm quark in the decay J/ψ→γφφ based on J/ψ data samples accumulated on the Beijing Electron Positron Collider (BEPC). The EDM and CDM interactions are introduced in this decay and then we relate them to some CP asymmetrical observables, which are predicted in the valence quark model We propose a method to hunt for these values by measuring associated CP asymmetrical observables, and we also discuss the prospect of such measurement on the BEPC.