Laser-induced desorption of water molecules from nanometer amorphous solid water films supported on a single-crystal platinum substrate is reported. A femtosecond laser pulse creates hot substrate electrons, which are injected into the water layer, resulting in significant desorption at the water-vacuum interface. The dependence of the desorption yield on film thickness and results for isotopic spacer and capping layers reveal that the desorbing water originates from relatively deep down into the water layer, i.e., from several nanometers below the surface. This is proposed to be the result of cooperative electronic effects resulting from the high electron densities in the thin water film, which cause a transient destabilization of the water H-bonded network. Motion of excited water molecules through the layer is enabled by mixing within the layer on ultrafast timescales during the desorption process.