Computer simulations of a special bond-fluctuation model are used to investigate the effects of chain topology on the dynamics of confined polymer melts. Short polymer chains with and without topological constraints exhibit nearly identical increases in relaxation times upon confinement. In longer chains, the effects of confinement are actually more pronounced for chains without topological constraints. These results suggest that entanglements are neither induced nor enhanced by confinement between impenetrable adsorbing surfaces. Implications of these results for rheological theories of confined polymer melts are discussed.