  We compile observations of molecular gas contents and infrared-based star
formation rates (SFRs) for 112 circumnuclear star forming regions, in order to
re-investigate the form of the disk-averaged Schmidt surface density star
formation law in starbursts. We then combine these results with total gas and
SFR surface densities for 153 nearby non-starbursting disk galaxies from de los
Reyes \& Kennicutt (2019), to investigate the properties of the combined star
formation law, following Kennicutt (1998; K98). We confirm that the combined
Schmidt law can be fitted with a single power law with slope $n = 1.5\pm0.05$
(including fitting method uncertainties), somewhat steeper than the value $n =
1.4\pm0.15$ found by K98. Fitting separate power laws to the non-starbursting
and starburst galaxies, however, produces very different slopes ($n =
1.34\pm0.07$ and $0.98\pm0.07$, respectively), with a pronounced offset in the
zeropoint ($\sim$0.6\,dex) of the starburst relation to higher SFR surface
densities. This offset is seen even when a common conversion factor between CO
intensity and molecular hydrogen surface density is applied, and is confirmed
when disk surface densities of interstellar dust are used as proxies for gas
measurements. Tests for possible systematic biases in the starburst data fail
to uncover any spurious sources for such a large offset. We tentatively
conclude that the global Schmidt law in galaxies, at least as it is
conventionally measured, is bimodal or possibly multi-modal. Possible causes
may include changes in the small-scale structure of the molecular ISM or the
stellar initial mass function. A single $n \sim 1.5$ power law still remains as
a credible approximation or "recipe" for analytical or numerical models of
galaxy formation and evolution.
