  The direct observation of time reversal symmetry violation (TV) is important
for the test of $CPT$ conservation and the Standard Model. In this paper, we
study both time-dependent and time-independent genuine TV signals in entangled
$D^0-\bar{D}^0$ pairs. A possible $CPT$-violation effect called the $\omega$
effect is also investigated. In the $C=-1$ entangled state, the asymmetries due
to TV are calculated to be of the order of $10^{-5}$ to $10^{-4}$ within the
Standard Model, but the modification due to the $\omega$ effect in the $C=-1$
states is found to be about $10\%-30\%$ when $|\omega|\sim 10^{-4}$. This
result is consistent with our Monte Carlo simulation, which implies that with
$10^9$ to $10^{10}$ events, TV signals can be observed in the entangled
$D^0-\bar{D}^0$ pairs, and the bound of $\omega \sim 10^{-3}$ can be reached.
The time-dependent and the time-independent asymmetries in the $C=-1$
$D^0-\bar{D}^0$ system provides a window to detect new physics such as the
$\omega$ effect, although they are not easily observable.
