We present Karl G. Jansky Very Large Array (VLA) Ka band (33 GHz) and Atacama Large Millimeter Array (ALMA) Band 3 (94.5 GHz) continuum images covering the nucleus and two extranuclear star-forming regions within the nearby galaxy NGC 3627 (M 66), observed as part of the Star Formation in Radio Survey (SFRS). Both images achieve an angular resolution of $lesssim$2arcsec, allowing us to map the radio spectral indices and estimate thermal radio fractions at a linear resolution of $lesssim$90 pc at the distance of NGC 3627. The thermal fraction at 33 GHz reaches unity at and around the peaks of each HII region; we additionally observed the spectral index between 33 and 94.5 GHz to become both increasingly negative and positive away from the peaks of the HII regions, indicating an increase of non-thermal extended emission from diffusing cosmic-ray electrons and the possible presence of cold dust, respectively. While the ALMA observations were optimized for collecting continuum data, they also detected line emission from the $J=1rightarrow0$ transitions of HCN and HCO$^{+}$. The peaks of dense molecular gas traced by these two spectral lines are spatially offset from the peaks of the 33 and 94.5 GHz continuum emission for the case of the extranuclear star-forming regions, indicating that our data reach an angular resolution at which one can spatially distinguish sites of recent star formation from the sites of future star formation. Finally, we find trends of decreasing dense gas fraction and velocity dispersion with increasing star formation efficiency among the three regions observed, indicating that the dynamical state of the dense gas, rather than its abundance, plays a more significant role in the star formation process.
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