  We reconsider the extrinsic and possible intrinsic CPT violation in neutrino
oscillations, and point out an identity, i.e., $A^{\rm CP}_{\alpha \beta} =
A^{\rm CPT}_{\beta \alpha} + A^{\rm T}_{\alpha \beta}$, among the CP, T, and
CPT asymmetries in oscillations. For three-flavor oscillations in matter of
constant density, the extrinsic CPT asymmetries $A^{\rm CPT}_{ee}$, $A^{\rm
CPT}_{e\mu}$, $A^{\rm CPT}_{\mu e}$, and $A^{\rm CPT}_{\mu \mu}$ caused by
Earth matter effects have been calculated in the plane of different neutrino
energies and baseline lengths. It is found that two analytical conditions can
be implemented to describe the main structure of the contours of vanishing
extrinsic CPT asymmetries. Finally, without assuming intrinsic CPT symmetry in
the neutrino sector, we investigate the possibility to constrain the difference
of the neutrino CP-violating phase $\delta$ and the antineutrino one
$\overline{\delta}$ using a low-energy neutrino factory and the super-beam
experiment ESS$\nu$SB. We find that $|\delta - \overline{\delta}| \lesssim
0.35\pi$ in the former case and $|\delta - \overline{\delta}| \lesssim 0.7\pi$
in the latter case can be achieved at the $3\sigma$ confidence level if $\delta
= \overline{\delta} = \pi/2$ is assumed.
