The superfluid response of helium films with transition temperatures ranging from 70 mK to 0.5 K has been studied using a torsional oscillator technique. A detailed analysis of the background indicates that the initial nonsuperfluid layer has an unexpected temperature-dependent period shift and dissipation. The superfluid response obeys a general scaling law which can be derived from the Kosterlitz-Thouless theory. Comparisons with the dynamic theory reveal nonuniversal behavior as a function of coverage. 1989 The American Physical Society.