A sensitive observation of the CO J=1-0 molecular line emission in the host galaxy of GRB 030329 (z=0.1685) has been performed using the Nobeyama Millimeter Array to detect molecular gas and hidden star formation. No sign of CO emission was found, which invalidates our previous report of the presence of molecular gas. The 3 σ upper limit on the CO line luminosity (L'CO) of the host galaxy is 6.9×108 K km s-1 pc2. The lower limit to the host galaxy's metallicity is estimated to be 12+log(O/H)~7.9, which yields a conversion factor from CO line luminosity to H2 of αCO=40 Msolar (K km s-1 pc2)-1. Assuming this factor, the 3 σ upper limit on the molecular gas mass of the host galaxy is 2.8×1010 Msolar. Based on the Schmidt law, the 3 σ upper limit on the total star formation rate (SFR) of the host galaxy is estimated to be 38 Msolar yr-1. These results independently confirm inferences from previous observations in the optical, submillimeter, and X-ray bands, which regard this host galaxy as a compact dwarf and not a massive, aggressively star-forming galaxy. Finally, the SFRs of GRB host galaxies, estimated using various techniques immune to dust obscuration, including our CO luminosity measurements, are compared with the SFRs of the same galaxies estimated using extinction-corrected optical/UV tracers. We show that most of the SFRs measured in extinction-free wavelengths, including positive detections and upper limits, are larger by from 1 to a few orders of magnitude compared with the SFRs of the same galaxies measured by optical/UV tracers.
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