We analyze the central discontinuous Galerkin (DG) method for
time-dependent linear conservation laws. In one dimension, optimal a priori $L^2$ error
estimates of order $k+1$ are obtained for the semidiscrete
scheme when piecewise polynomials of degree at most
$k$ ($k\geq0$) are used on overlapping uniform meshes.
%Our analysis is valid for both periodic boundary conditions and
%for inflow-outflow boundary conditions.
We then extend the analysis to multidimensions on uniform Cartesian
meshes when piecewise tensor product polynomials are used on
overlapping meshes. Numerical experiments are given to
demonstrate the theoretical results.