Superconductivity was recently found in the tetragonal phase FeSe. A structural transformation from tetragonal to orthorhombic (or monoclinic, depending on point of view) was observed at low temperature, but was not accompanied by a magnetic ordering as commonly occurs in the parent compounds of FeAs-based superconductors. Here, we report the correlation between structural distortion and superconductivity in FeSe(1-x) thin films with different preferred growth orientations. The films with preferred growth along the c axis show a strong thickness dependent suppression of superconductivity and low temperature structural distortion. In contrast, both properties are less affected in the films with (101) preferred orientation. These results suggest that the low temperature structural distortion is closely associated with the superconductivity of this material.