The high-resolution laser excitation spectrum of the 001-000 and 000-000 bands of the B̃2Σ+-X̃2Σ+ transition of SrOD was recorded. The SrOD molecules were made by pulsed laser ablation of Sr metal followed by reaction with D2O. Sub-Doppler resolution and rotational cooling were achieved by expansion into vacuum and excitation with a cw dye laser perpendicular to the molecular beam. A molecular linewidth of 200 MHz and the lack of spectral congestion allowed a Q branch to be detected. Spin-orbit mixing between the Ã2Π and B̃2Σ+ states caused the unusual appearance of a moderate intensity Q branch in a nominally parallel 2Σ+-2+ transition. From the relative intensities of the rotational lines, the ratio of the perpendicular to the parallel transition dipole moment was found to be 0.2 to 0.3.