We performed a sensitive search for the ground-state emission lines of ortho- and para-water vapor in the DM Tau protoplanetary disk using the Herschel/HIFI instrument. No strong lines are detected down to 3σ levels in 0.5 km s-1 channels of 4.2 mK for the 110-101 line and 12.6 mK for the 111-000 line. We report a very tentative detection, however, of the 110-101 line in the wide band spectrometer, with a strength of Tmb = 2.7 mK, a width of 5.6 km s-1 and an integrated intensity of 16.0 mK km s-1. The latter constitutes a 6σ detection. Regardless of the reality of this tentative detection, model calculations indicate that our sensitive limits on the line strengths preclude efficient desorption of water in the UV illuminated regions of the disk. We hypothesize that more than 95-99% of the water ice is locked up in coagulated grains that have settled to the midplane. Herschel is an ESA space observatory with science instruments provided by European-led Principal Investigator consortia and with participation important from NASA.