The transfer reaction 94 Zr͑d,p͒ 95 Zr has been studied to check the existence of a low-lying first excited level at 23 keV in 95 Zr. This level-if it exists-might have significant influence on the branching of the astrophysical s process at the branching nucleus 95 Zr. Our experimental spectra, measured with very good energy resolution, do not show any evidence for the existence of such a low-lying level. This is in agreement with experimental results from several reactions and contradicts the only claim for evidence of such a low-lying level which was also derived from 94 Zr͑d,p͒ 95 Zr data, however with moderate resolution, but still the best of the previous experiments.