We report a search for emissions from the OH Meinel system in high-resolution near-infrared spectra of comet P/Swift-Tuttle. Because of the large cometary heliocentric velocity and high resolution of the spectrograph, the cometary lines should be well separated from the bright OH sky lines. Contrary to the findings of Tozzi et al. (1994) - who report seeing cometary OH at intensities comparable to the sky emissions in their low-resolution spectra - we find no OH in these spectra with an upper limit of 5% the value of the night sky lines. The non-detection of these cometary lines is consistent with theoretical calculations of expected emission strengths from prompt and fluorescent emission from cometary OH.