  We present a search for CO(3-2) emission in SDF-26821, a BzK-selected
star-forming galaxy (sBzK) at z = 2.044, using the 45-m telescope of the
Nobeyama Radio Observatory and the Nobeyama Millimeter Array. We do not detect
significant emission and derive 2 \sigma limits: the CO luminosity of L'CO <
3.1 x 10^10 K km s^{-1} pc^{-2}, the ratio of far-infrared luminosity to CO
luminosity of L_FIR/L'CO > 57 Lsun (K km s^{-1} pc^{-2})^{-1}, and the
molecular gas mass of M_H2 < 2.5 x 10^10 Msun, assuming a velocity width of 200
km s^{-1} and a CO-to-H2 conversion factor of alpha_CO=0.8 Msun (K km s^{-1}
pc^{-2})^{-1}. The ratio of L_FIR/L'CO, a measure of star formation efficiency
(SFE), is comparable to or higher than the two z ~ 1.5 sBzKs detected in
CO(2-1) previously, suggesting that sBzKs can have a wide range of SFEs.
Comparisons of far-infrared luminosity, gas mass, and stellar mass among the
sBzKs suggest that SDF-26821 is at an earlier stage of forming stars with a
similar SFE and/or more efficiently forming stars than the two z ~ 1.5 sBzKs.
The higher SFEs and specific star formation rates of the sBzKs compared to
local spirals are indicative of the difference in star formation modes between
these systems, suggesting that sBzKs are not just scaled-up versions of local
spirals.
