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 $n = 1.5pm0.05$ (including fitting method uncertainties), somewhat steeper than the value $n = 1.4pm0.15$ found by K98. Fitting separate power laws to the non-starbursting and starburst galaxies, however, produces very different slopes ($n = 1.34pm0.07$ and $0.98pm0.07$, 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.
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