  We search for CP violation in a sample of $4.7\times10^4$ Cabibbo-suppressed
$D^0 \to K^+ K^- \pi^+ \pi^-$ decays. We use 470{\rm fb}^{-1} of data recorded
by the BaBar detector at the PEPII asymmetric-energy $e^+e^-$ storage rings
running at center-of-mass energies near 10.6 GeV. CP violation is searched for
in the difference between the $T$-odd asymmetries, obtained using triple
product correlations, measured for $D^0$ and $\bar D^0$ decays. The measured CP
violation parameter is ${\cal A}_T = (1.0 \pm 5.1_{\sta}\pm 4.4_{\sys}) \times
10^{-3}$.
