Effects of initial orbital alignment have been investigated for the fine-structure transitions of Hg(6(3)P(1) --> 6(3)P(0)) induced by collisions with N-2 and CO in a crossed molecular beam experiment using a laser pump-probe technique. The orbital alignment effects are observed by monitoring the population of the product Hg(6(3)P(0)) as a function of polarization angle (theta) of the linearly polarized pump laser, which prepares the Hg(6(3)P(1)), relative to the direction of the initial relative velocity vector. The alignment effects in this study are represented by an asymmetry parameter beta in the angle-dependent cross section, sigma(theta) = sigma(0)[1 + beta P-2(cos theta)]. The measurement for Hg-N-2 exhibits a large alignment effect with beta = -0.50(7), but for Hg-CO a small effect with beta = -0.20(6). Both processes show preference for perpendicular excitation of the pump laser with theta = 90 degrees. The nonadiabatic transitions responsible for this fine-structure process therefore occur mainly via the (B) over tilde(2(3)A＇ + 2(3)A ") molecular electronic state and not via the (A) over tilde(1(3)A＇) state for Hg-N-2. In contrast, the small effect for Hg-CO indicates that the contribution from the nonadiabatic transition via the A state is comparable with that via the (B) over tilde state for Hg-CO.