The adsorption of thin water overlayers on the (101) surface of TiO2 anatase has been Studied through Car-Parrinello molecular dynamics (CPMD) simulations. We compared the Structural and dynamic properties of one and two H2O monolayers adsorbed on defect-free and partially reduced surfaces at 160 K. As for an isolated adsorbed H2O molecule, We found that water dissociation is possible only on the defective surface. With respect to a single H2O, the interaction between H2O molecules reduces the dissociation barrier: a water molecule incorporated in a monolayer (ML) or a bilayer (BL) over a defected surface dissociates spontaneously at 160 K. On the perfect Surface, a water ML forms a regular array of Ti-coordinated molecules, whereas on the defective Surface some molecules shift coordination from Ti to a bridging (O-2c) oxygen, leading to a mixed ML state with molecular water adsorbed on two different sites and two hydroxyls resulting from the dissociation. Only after adsorption of a second water layer O-2c-coordinated molecules are formed also on the regular surface, leading to a more disordered state. Although most structural differences between water overlayers on defect-free and defective surfaces disappear at BL coverage, water molecules are more mobile in the presence of the defect. The presence of H2O-O-2c only above ML coverage and the lack of water dissociation oil the defect-free surface are in agreement with the findings of recent temperature-programmed desorption experiments, which have been further analyzed on the basis of the calculated adsorption energies.