  The paper aims to investigate curvature inheritance symmetry in
M-projectively flat spacetimes. It is shown that the curvature inheritance
symmetry in M-projectively flat spacetime is a conformal motion. We have proved
that M- projective curvature tensor follows the symmetry inheritance property
along a vector field $\xi$, when spacetime admits the conditions of both
curvature inheritance symmetry and conformal motion or motion along the vector
field $\xi$. Also, we have derived some results for M-projectively flat
spacetime with perfect fluid following the Einstein field equations with a
cosmological term and admitting the curvature inheritance symmetry along the
vector field $\xi$. We have shown that an M-projectively flat perfect fluid
spacetime obeying the Einstein field equations with a cosmological term and
admitting the curvature inheritance symmetry along a vector field $\xi$ is
either a vacuum or satisfies the vacuum-like equation of state. We have also
shown that such spacetimes with the energy momentum tensor of an
electromagnetic field distribution do not admit any curvature symmetry of
general relativity. Finally, an example of M-projectively flat spacetime has
been exhibited.
