  We present a search for signatures of neutrino mixing of electron
anti-neutrinos with additional hypothetical sterile neutrino flavors using the
Double Chooz experiment. The search is based on data from 5 years of operation
of Double Chooz, including 2 years in the two-detector configuration. The
analysis is based on a profile likelihood, i.e.\ comparing the data to the
model prediction of disappearance in a data-to-data comparison of the two
respective detectors. The analysis is optimized for a model of three active and
one sterile neutrino. It is sensitive in the typical mass range $5 \cdot
10^{-3} $ eV$^2 \lesssim \Delta m^2_{41} \lesssim 3\cdot 10^{-1} $ eV$^2$ for
mixing angles down to $\sin^2 2\theta_{14} \gtrsim 0.02$. No significant
disappearance additionally to the conventional disappearance related to
$\theta_{13} $ is observed and correspondingly exclusion bounds on the sterile
mixing parameter $\theta_{14} $ as function of $ \Delta m^2_{41} $ are
obtained.
