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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 KEKBenergy-asymmetric $e^+e^-$ collider. Our results for the $T$-odd$C\!P$-violating parameter $a^{T\text{-odd}}_{C\!P}$ are:$a^{T\text{-odd}}_{C\!P}({D^{+}\to K^{-}K^{+}\pi^{+}\pi^{0}}) = (+2.6\pm 6.6\pm1.3 )\times10^{-3}$, $a^{T\text{-odd}}_{C\!P}({D^{+}\toK^{+}\pi^{-}\pi^{+}\pi^{0}}) = (-1.3\pm 4.2\pm 0.1 )\times10^{-2}$,$a^{T\text{-odd}}_{C\!P}({D^{+}\to K^{-}\pi^{+}\pi^{+}\pi^{0}}) = (+0.2\pm1.5\pm 0.8 )\times10^{-3}$, $a^{T\text{-odd}}_{C\!P}({D_s^{+}\toK^{+}\pi^{-}\pi^{+}\pi^{0}}) = (-1.1\pm 2.2\pm 0.1 )\times10^{-2}$, and$a^{T\text{-odd}}_{C\!P}({D_s^{+}\to K^{-}K^{+}\pi^{+}\pi^{0}}) = (+2.2\pm3.3\pm 4.3 )\times10^{-3}$, where the uncertainties are statistical andsystematic, respectively. These results are the first such measurements and areall consistent with zero. They include the first measurement for a $D^+_s$singly Cabibbo-suppressed decay, and the first measurement for a $D$ mesondoubly Cabibbo-suppressed decay. We also measure $a^{T\text{-odd}}_{C\!P}$ indifferent subregions of phase space, where the decays are dominated bydifferent 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.

Search for $C\!P$ violation using $T$-odd correlations in  $D_{(s)}^{+}\to K^{+} K^{-}\pi^{+}\pi^{0}$, $D_{(s)}^{+}\to K^{+}  \pi^{-}\pi^{+}\pi^{0}$, and $D^{+}\to K^{-}\pi^{+}\pi^{+}\pi^{0}$ decays