  We study the finite-size corrections of the dimer model on $\infty \times N$
square lattice with two different boundary conditions: free and periodic. We
find that the finite-size corrections depend in a crucial way on the parity of
$N$, and show that, because of certain non-local features present in the model,
a change of parity of $N$ induces a change of boundary condition. Taking a
careful account of this, these unusual finite-size behaviours can be fully
explained in the framework of the $c=-2$ logarithmic conformal field theory.
