  Taking as starting point a Lorentz and CPT non-invariant Chern-Simons-like
model defined in 1+3 dimensions, we proceed realizing its dimensional reduction
to D=1+2. One then obtains a new planar model, composed by the
Maxwell-Chern-Simons (MCS) sector, a Klein-Gordon massless scalar field, and a
coupling term that mixes the gauge field to the external vector, $v^{\mu}$. In
spite of breaking Lorentz invariance in the particle frame, this model may
preserve the CPT symmetry for a single particular choice of $v^{\mu}$.
Analyzing the dispersion relations, one verifies that the reduced model
exhibits stability, but the causality can be jeopardized by some modes. The
unitarity of the gauge sector is assured without any restriction, while the
scalar sector is unitary only in the space-like case.
  PACS numbers: 11.10.Kk; 11.30.Cp; 11.30.Er; 12.60.-i
