  We present the first statistical survey of the properties of the 12CO(1-0)
and 12CO(3-2) line emission from the nuclei of a nearly complete subsample of
60 infrared (IR) luminous galaxies selected from SCUBA Local Universe Galaxy
Survey (SLUGS). This subsample is flux limited at S60 mincron > 5.24 Jy with
far-IR (FIR) luminosities mostly at LFIR > 10^10 LSUN. We compare the emission
line strengths of 12CO(1-0) and (3-2) transitions at a common resolution of
15". The measured 12CO(3-2) to (1-0) line intensity ratios r31 vary from 0.22
to 1.72 with a mean value of 0.66 for the sources observed, indicating a large
spread of the degree of excitation of CO in the sample. These CO data, together
with a wide range of data at different wavelengths obtained from the
literature, allow us to study the relationship between the CO excitation
conditions and the physical properties of gas/dust and star formation in the
central regions of galaxies. Our analysis shows that there is a non-linear
relation between CO and FIR luminosities, such that their ratio LCO/LFIR
decreases linearly with increasing LFIR. This behavior was found to be
consistent with the Schmidt Law relating star formation rate to molecular gas
content, with an index N = 1.4 +- 0.3. We also find a possible dependence of
the degree of CO gas excitation on the efficiency of star forming activity.
Using the large velocity gradient (LVG) approximation to model the observed
data, we investigate the CO-to-H2 conversion factor X for the SLUGS sample. The
results show that the mean value of X for the SLUGS sample is lower by a factor
of 10 compared to the conventional value derived for the Galaxy, if we assume
the abundance of CO relative to H2, ZCO = 10^-4.
