We report the negative results from a search for 6.7 GHz methanol masers in
the nearby spiral galaxy M33. We observed 14 GMCs in the central 4 kpc of the
Galaxy, and found 3 sigma upper limits to the flux density of ~9 mJy in
spectral channels having a velocity width of 0.069 km/s. By velocity shifting
and combining the spectra from the positions observed, we obtain an effective
3sigma upper limit on the average emission of ~1mJy in a 0.25 km/s channel.
These limits lie significantly below what we would expect based on our
estimates of the methanol maser luminosity function in the Milky Way. The most
likely explanation for the absence of detectable methanol masers appears to be
the metallicity of M33, which is modestly less than that of the Milky Way