A general expression for the Doppler profile for fragments produced in the photodissociation of laser excited, aligned molecules, as in vibrationally mediated photodissociation (VMP), is presented. In contrast to one-photon dissociation, for which the Doppler profile depends only on the second moment of the fragment molecular-frame angular distribution, the profile in the case of VMP is sensitive to several moments of the angular distribution, up to k=4. In addition, the profile for a near-prolate molecule depends on the angle theta(a) between the electronic transition moment mu and the a inertial axis. This theory is applied to the analysis and interpretation of Doppler profiles in the laser fluorescence detection of NH(a (1)Delta) fragments, of rotational angular momenta N=7 and 10, from the 532 nm VMP of HN3 excited to the second N-H stretch overtone level (3 nu(1)). For both Lambda-doublets of these rotational levels, the second moment of the molecular-frame angular distribution beta(2,0)=[P-2(cos theta(m))] was found to be positive, in agreement with previous results for high-J fragments from one-photon photolysis of HN3. The profiles are consistent with a value of similar to 0 degrees for the angle theta(a). These values for theta(a) and beta(2,0) are inconsistent with simple expectations based on planar, prompt dissociation upon excitation to the lowest singlet excited state ((1)A ") and suggest the importance of nonplanar geometries in the dissociation dynamics.