We analyze the conditions for detection of CO(1-0) emission in the Large Magellanic Cloud (LMC), using the recently completed second NANTEN CO survey. In particular, we investigate correlations between CO integrated intensity and HI integrated intensity, peak brightness temperature, and line width at a resolution of 2.6 (~40 pc). We find that significant HI column density and peak brightness temperature are necessary but not sufficient conditions for CO detection, with many regions of strong HI emission not associated with molecular clouds. The large scatter in CO intensities for a given HI intensity persists even when averaging on scales of >200 pc, indicating that the scatter is not solely due to local conversion of HI into H_2 near GMCs. We focus on two possibilities to account for this scatter: either there exist spatial variations in the I(CO) to N(H_2) conversion factor, or a significant fraction of the atomic gas is not involved in molecular cloud formation. A weak tendency for CO emission to be suppressed for large HI linewidths supports the second hypothesis, insofar as large linewidths may be indicative of warm HI, and calls into question the likelihood of forming molecular clouds from colliding HI flows. We also find that the ratio of molecular to atomic gas shows no significant correlation (or anti-correlation) with the stellar surface density, though a correlation with midplane hydrostatic pressure P_h is found when the data are binned in P_h. The latter correlation largely reflects the increasing likelihood of CO detection at high HI column density.
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