I report the density-matrix renormalization group computation of the equal-time single-particle Green's function and the density-density correlations of a spinless fermion model in an anisotropic two-dimensional lattice at half-filling. I find that the dominant correlations are single-particle correlations. The density-density correlations do not show any sign of long-range charge-density-wave order. This implies a Fermi-liquid ground state.