We revisit the issue of a correlation between the atomic hydrogen gas in our local Galaxy and the Cosmic Microwave Background (CMB), a detection of which has been claimed in some literature. We cross-correlate the 21-cm emission of Galactic atomic hydrogen as traced by the Leiden/Argentine/Bonn Galactic HI survey with the 3-year CMB data from the Wilkinson Microwave Anisotropy Probe. We consider a number of angular scales, masks, and HI velocity slices and find no statistically significant correlation.