In the light of a recent theoretical study claiming partial dissociation of water on Ru(0 0 1) [Science 295 (2002) 99], the adsorption of the first layers of H2O and D2O on Ru(0 0 1) is investigated using an especially sensitive temperature programmed desorption technique. Hydrogen desorption following thermal desorption of molecular water is used to analyze the amount of atomic hydrogen (H or D) remaining on the ruthenium surface as a function of initial H2O or D2O coverage, respectively. For both water isotopomeres atomic hydrogen is observed to remain on the surface after water desorption, indicating that dissociative adsorption is taking place at least to a small extent for both H2O and D2O. In the framework of the proposed half-dissociated water structure by Feibelman, the H2:D2 ratio of ~26 for the maximum hydrogen yield might be a consequence of an isotope effect in the recombinative desorption of water due to the different adsorption superstructures for H2O and D2O as reported by Held and Menzel [Phys. Rev. Lett. 74 (1995) 4221].