  We search for $C\!P$ violation using $T$-odd correlations in five
$D_{(s)}^{+}$ and $D_{(s)}^{-}$ four-body decays. Our analysis is based on 980
$\rm fb^{-1}$ of data collected by the Belle detector at the KEKB
energy-asymmetric $e^+e^-$ collider. Our results for the $T$-odd
$C\!P$-violating parameter $a^{T\text{-odd}}_{C\!P}$ are:
$a^{T\text{-odd}}_{C\!P}({D^{+}\to K^{-}K^{+}\pi^{+}\pi^{0}}) = (+2.6\pm 6.6\pm
1.3 )\times10^{-3}$, $a^{T\text{-odd}}_{C\!P}({D^{+}\to
K^{+}\pi^{-}\pi^{+}\pi^{0}}) = (-1.3\pm 4.2\pm 0.1 )\times10^{-2}$,
$a^{T\text{-odd}}_{C\!P}({D^{+}\to K^{-}\pi^{+}\pi^{+}\pi^{0}}) = (+0.2\pm
1.5\pm 0.8 )\times10^{-3}$, $a^{T\text{-odd}}_{C\!P}({D_s^{+}\to
K^{+}\pi^{-}\pi^{+}\pi^{0}}) = (-1.1\pm 2.2\pm 0.1 )\times10^{-2}$, and
$a^{T\text{-odd}}_{C\!P}({D_s^{+}\to K^{-}K^{+}\pi^{+}\pi^{0}}) = (+2.2\pm
3.3\pm 4.3 )\times10^{-3}$, where the uncertainties are statistical and
systematic, respectively. These results are the first such measurements and are
all consistent with zero. They include the first measurement for a $D^+_s$
singly Cabibbo-suppressed decay, and the first measurement for a $D$ meson
doubly Cabibbo-suppressed decay. We also measure $a^{T\text{-odd}}_{C\!P}$ in
different subregions of phase space, where the decays are dominated by
different intermediate resonance states such as $D^+\to\phi\rho^+$,
$\bar{K}^{*0}K^{*+}$, and $\bar{K}^{*0}\rho^+$; and $D_s^+\to K^{*+}\rho^{0}$,
$K^{*0}\rho^{+}$, $\phi\rho^+$, and $\bar{K}^{*0}K^{*+}$. No evidence for
$C\!P$ violation is found.
