  Aims: We present new radio continuum observations of ten BIMA SONG galaxies,
taken at 1.4 GHz with the Very Large Array. These observations allow us to
extend the study of the relationships between the radio continuum (RC) and CO
emission to 22 CO luminous galaxies for which single dish CO images have been
added to interferometric data. New Spitzer infrared (IR) images of six of these
galaxies have been released. The analysis of these high resolution images
allowed us to probe the RC-IR-CO correlations down to linear scales of a few
hundred pc. Results: for the 22 galaxies analysed, the RC-CO correlation on
scales from $\sim10$ kpc down to $\sim100$ pc is nearly linear and has a
scatter of a factor of two, i.e. comparable to that of the global correlations.
There is no evidence for any severe degradation of the scatter below the kpc
scale. This also applies to the six galaxies for which high-resolution mid-IR
data are available. In the case of NGC 5194, we find that the non-thermal radio
spectral index is correlated with the RC/FIR ratio. Conclusions: The scatter of
the point-by-point correlations does not increase significantly with spatial
resolution. We thus conclude that we have not yet probed the physical scales at
which the correlations break down. However, we observe local deviations from
the correlations in regions with a high star formation rate, such as the spiral
arms, where we observe a flat radio spectrum and a low RC/FIR ratio. In the
intra-arm regions and in the peripheral regions of the disk, the RC/FIR is
generally higher and it is characterized by a steepening of the radio spectrum.
