High-resolution zero-kinetic-energy photoelectron spectroscopy has been used to record the transition between the lowest bound state (3s (2)A(1)) of the perdeuterated ammonium radical (ND4) and the (X) over tilde (1)A(1) ground vibronic state of the perdeuterated ammonium ion (ND4+). The spectra obtained are the first rotationally resolved photoelectron spectra ever measured for a tetrahedral molecule. The analysis of the rotational structure is accompanied by a description of the observed symmetry selection rules and propensity rules for core rotational angular momentum changes that characterize the photoionization process. Rotational constants (B-0 = 2.8560 +/- 0.0037 cm(-1) and B-0(+) = 2.9855 +/- 0.0037 cm(-1)) and centrifugal distoration constants (D-0 = (4.78 +/- 1.4) x 10(-5) cm(-1) and D-0(+) = (4.77 +/- 1.5) x 10(-5) cm(-1)) have been determined for the 3s (2)A(1) state of ND4 and the (X) over tilde(1)A(1) state ND4+, respectively. The ionic rotational constant is in good agreement with the value B-0(+) = 2.9787 +/- 0.0029 cm(-1) determined indirectly by Crofton and Oka (J. Chem. Phys. 86, 5983 (1987)) from the measurement of allowd transitions of the v(3) vibrational band of ND4+. The neutralrotational constant differs markedly from the ab initio value B-0= 3.0407 cm(-1) of Havriliak and King (J. Am. Chem. Sec. 105, 4 (1983)) used by Alberti, Huber and Watson (J. Mel. Spectrosc. 107, 133 (1984)) as input data to fit the rotational structure of the Schuler band of ND4. The adiabatic ionization potential of ND4 is determined to be 37490.7 +/- 1.5 cm(-1) (4.64826 +/- 0.00019 eV). The large changes in core rotational angular momentum that accompany the removal of the photoelectron may be caused by the (looper minimum in the s --> p photoexcitation/photoionization channel recently predicted by Smith and Chupka [Chem. Phys. Lett. 250, 589 (1996)] to lie in the vicinity of the ionization threshold.