We investigate the origin of the parsec-scale radio emission from the changing-look active galactic nucleus (AGN) of Mrk 590, and examine whether the radio power has faded concurrently with the dramatic decrease in accretion rates observed between the 1990s and the present. We detect a compact core at 1.6 GHz and 8.4 GHz using new Very Long Baseline Array observations, finding no significant extended, jet-like features down to $sim$1 pc scales. The flat spectral index ($alpha_{1.6}^{8.4} = 0.03$) and high brightness temperature ($T_{rm b} sim 10^{8},rm K$) indicate self-absorbed synchrotron emission from the AGN. The radio to X-ray luminosity ratio of ${rm log}(L_{rm R}/L_{rm X}) sim -5$, similar to that in coronally active stars, suggests emission from magnetized coronal winds, although unresolved radio jets are also consistent with the data. Comparing new Karl G. Jansky Very Large Array measurements with archival and published radio flux densities, we find $46%$, $34%$, and (insignificantly) $13%$ flux density decreases between the 1990s and the year 2015 at 1.4 GHz, 5 GHz and 8.4 GHz respectively. This trend, possibly due to the expansion and fading of internal shocks within the radio-emitting outflow after a recent outburst, is consistent with the decline of the optical-UV and X-ray luminosities over the same period. Such correlated variability demonstrates the AGN accretion-outflow connection, confirming that the changing-look behaviour in Mrk 590 originates from variable accretion rates rather than dust obscuration. The present radio and X-ray luminosity correlation, consistent with low/hard state accretion, suggests that the black hole may now be accreting in a radiatively inefficient mode.
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