We combine 12CO J = 3 - 2 for 155 nearby galaxies, obtained as part of the James Clerk Maxwell Telescope (JCMT) Nearby Galaxies Legacy Survey (NGLS), with star formation rates derived from Hα luminosities to probe the relation between warm, dense gas and star formation. These data are compared with ancillary data from the literature, including infrared (IR) and 1.4 GHz radio continuum luminosities and Hi masses. We find a good correlation between CO J = 3 - 2 luminosities and Hα-derived star formation rates (SFRs), which is in agreement with previous studies. Several groups of galaxies show a peculiar behaviour in the SFR(Hα) - L CO J = 3 - 2 plot, which disappears when using IR data. We analyse these regions and propose several hypotheses to explain this behaviour, including group interactions and very recent (≲20 Myr) bursts of star formation only traced by Hα emission. While atomic hydrogen is hardly related with SFR, molecular and total gas (Hi + H2) show similar correlations with Hα luminosities. No correlation is found between CO J = 3-2 luminosity and metallicity, although galaxies with low metallicity are more likely to not be detected. We discuss that CO J = 3 - 2 does not seem to be a significantly better tracer of the star-forming gas, but its independence from metallicity may be used to constrain the conversion factor between CO and H2.