We report a measurement of $CP$ violating asymmetries in $B^0(overline{B}^0) to K^+ K^- K^0_S$ decays with a time-dependent Dalitz approach. This analysis is based on a data sample of $657times 10^6$ $Boverline{B}$ pairs accumulated at the $Upsilon(4
S)$ resonance with the Belle detector at the KEKB asymmetric-energy $e^+e^-$ collider. As the result of an unbinned maximum likelihood fit to the selected candidates, the mixing-induced and direct $CP$ violation parameters, $phi^{rm eff}_1$ and ${cal A}_{CP}$ are obtained for $B^0 to phi(1020) K^0_S$, $B^0 to f_0(980) K^0_S$ and other $B^0 to K^+ K^- K^0_S$ decays. We find four solutions that describe the data. There are {eqnarray*} phi_1^{rm eff}(B^0to phi(1020) K^0_S) & = & (32.2 pm 9.0 pm 2.6 pm 1.4)^{circ}; phi_1^{rm eff}(B^0to phi(1020) K^0_S) & = & (26.2 pm 8.8 pm 2.7 pm 1.2)^{circ}; phi_1^{rm eff}(B^0to phi(1020) K^0_S) & = & (27.3 pm 8.6 pm 2.8 pm 1.3)^{circ}; {rm and} phi_1^{rm eff}(B^0to phi(1020) K^0_S) & = & (24.3 pm 8.0 pm 2.9 pm 5.2)^{circ}.{eqnarray*} The values for the $CP$ violating phase in $B^0to phi(1020) K^0_S$ are similar but other properties of the Dalitz plot are quite different for the four solutions. These four solutions have consistent $phi^{rm eff}_1$ values for all three $B$ meson decay channels and none of them deviates significantly from the values measured in $B to (cbar{c}) K^0$ decays with the currently available statistics. In addition, we find no significant direct $CP$ violation.
