Collisional de-excitation rates of partially deuterated molecules are different from the fully hydrogenated species because of lowering of symmetry. We compute the collisional (de)excitation rates of ND2H by ground-state para-H2, extending the previous results for helium. We describe the changes in the potential energy surface of NH3–H2 involved by the presence of two deuterium nuclei. Cross-sections are calculated within the full close-coupling approach and augmented with coupled-state calculations. Collisional rate coefficients are given between 5 and 35 K, a range of temperatures which is relevant to cold interstellar conditions. We find that the collisional rates of ND2H by H2 are about 1 order of magnitude higher than those obtained with helium as perturber. These results are essential to radiative transfer modelling and will allow to interpret the millimetre and submillimetre detections of ND2H with better constraints than previously.