The H(D) Rydberg atom photofragment translational spectroscopy technique has been applied to a further detailed investigation of the photodissociation dynamics of NH3 and ND3 molecules following excitation to the lowest two (nu(2)=0 and 1) vibrational levels of the first excited ((A) over tilde (1)A "(2) singlet electronic state. Analysis of the respective total kinetic energy release spectra. recorded at a number of scattering angles Theta [where Theta is the angle between the epsilon vector of the photolysis photon and the time of-flight (TOF) axis], enables quantification of a striking, quantum state dependent, mu-nu correlation in the NH2(ND2) products. The spatial distribution of the total flux of H(D) atom photofragments is rather isotropic (beta(lab)similar to 0). However, more careful analysis of the way in which the TOF spectra of the H(D) atom photofragments vary with Theta reveals that each H+NH2(D+ND2) product channel has a different "partial" anisotropy parameter, beta(lab)(nu(2),N), associated with it : The H(D) atom ejected by those molecules that dissociate to yield NH2(ND2) fragments with little rotational excitation largely appear in the plane of the excited molecule (i.e., perpendicular to the transition moment and the C-3 axis of the parent, with beta tending towards -1). Conversely, the H(D) atoms formed in association with the most highly rotationally excited partner NH2(ND2) fragments tend to recoil almost parallel to this C-3 axis (i.e., beta-->+2). Such behavior is rationalized in the context of the known potential energy surfaces of the (A) over tilde and (X) over tilde states of ammonia using a classical, energy and angular momentum conserving impact parameter model in which we assume that all of the product angular momentum is established at the "point" of the conical intersection in the H-NH2(D-ND2) dissociation coordinate. We conclude by reemphasizing the level of care needed in interpreting experimentally measured beta parameters in situations where there is averaging over either the initial (parent) or final (product) quantum states.