Recently we developed a new microwave spectroscopy technique in the frequency range up to 40 GHz, and measured the static dielectric constant and the dielectric relaxation time for supercritical water. In the present work we report the dielectric properties of heavy water at temperatures and pressures up to 770 K and 59 MPa, respectively. The static dielectric constant of D2O as well as H2O are well described by the Uematsu-Franck formula when the number density instead of the mass density is used as the input parameter. The dielectric relaxation time decreases rapidly with increasing temperature in liquid H2O and D2O and jumps to a large value at the liquid-gas transition. The relaxation time of D2O is longer than that of H2O in the liquid state, and the difference becomes smaller with decreasing density in the gaseous state. For both H2O and D2O the most relevant parameter determining the relaxation time is the temperature at high densities or at low temperatures, and it is the density at low densities or at high temperatures. Based upon the observation that the dielectric relaxation time becomes fairly long in the dilute limit, we have concluded that the dielectric relaxation in the gaseous state is governed by the binary collision of water molecules and explained the relaxation time quantitatively by the collision time. We have extended the interpretation of the dielectric relaxation to the liquid state by taking into account the contribution of bound water molecules that are incorporated in the hydrogen-bond network. Anomalous relaxation at low temperatures is also discussed.