Search forCPviolation in the Dalitz-plot analysis ofD±→K+K−π±

We report on a search for $CP$ asymmetry in the singly Cabibbo-suppressed decay ${D}^{+}\ensuremath{\rightarrow}{K}^{+}{K}^{\ensuremath{-}}{\ensuremath{\pi}}^{+}$ using a data sample of $818\text{ }\text{ }{\mathrm{pb}}^{\ensuremath{-}1}$ accumulated with the CLEO-c detector on the $\ensuremath{\psi}(3770)$ resonance. A Dalitz-plot analysis is used to determine the amplitudes of the intermediate states. We find no evidence for $CP$ violation either in specific two-body amplitudes or integrated over the entire phase space. The $CP$ asymmetry in the latter case is measured to be $(\ensuremath{-}0.03\ifmmode\pm\else\textpm\fi{}0.84\ifmmode\pm\else\textpm\fi{}0.29)%$.