Nobeyama Millimeter Array was used to observe millimeter-wave afterglow of GRB 030329 at 93 GHz and 141 GHz from 2003 April 6 to 2003 May 30. A sensitive search for CO(J=1-0) emission/absorption from the host galaxy of GRB 030329 was also carried out. Unresolved millimeter continuum emission at the position of GRB 030329 was detected until 2003 April 21. We found a steep decline of continuum flux (propto t^{-2.0}) during this period, in accord with a previous report. Moreover, our data implies that the decay was accompanied by possible plateaus phases, or bumps, on a time scale of several days. From an integrated spectrum, produced by summing up the data from 2003 April 10 to 2003 May 30, we found a possible emission feature, which could be a redshifted CO(J=1-0) line. Its position and redshift coincide well with those of GRB 030329, though further observations are required to confirm the detection. If the emission feature is real, the observed CO flux is 1.4 +/- 0.52 Jy km/s, corresponding to a large molecular gas mass of M(H_2) > 10^9 Mo. This implies that the host galaxy, which is optically faint, is highly obscured due to a rich interstellar medium.
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