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ABSTRACT We present X-ray and radio observations of what may be the closest Type Iax supernova (SN) to date, SN 2014dt (d = 12.3–19.3 Mpc), and provide tight constraints on the radio and X-ray emission. We infer a specific radio luminosity $$L_R\lt (1.0\!-\!2.4)\times 10^{25}\, \rm {erg\, s^{-1}\, Hz^{-1}}$$ at a frequency of 7.5 GHz and a X-ray luminosity $$L_X\lt 1.4\times 10^{38}\, \rm {erg\, s^{-1}}$$ (0.3–10 keV) at ∼38–48 d post-explosion. We interpret these limits in the context of Inverse Compton (IC) emission and synchrotron emission from a population of electrons accelerated at the forward shock of the explosion in a power-law distribution $$N_e(\gamma _e)\propto \gamma _e^{-p}$$ with p = 3. Our analysis constrains the progenitor system mass-loss rate to be $$\dot{M}\lt 5.0 \times 10^{-6} \rm {M_{\odot }\, yr^{-1}}$$ at distances $$r\lesssim 10^{16}\, \rm {cm}$$ for an assumed wind velocity $$v_w=100\, \rm {km\, s^{-1}}$$, and a fraction of post-shock energy into magnetic fields and relativistic electrons of ϵB = 0.01 and ϵe = 0.1, respectively. This result rules out some of the parameter space of symbiotic giant star companions, and it is consistent with the low mass-loss rates expected from He-star companions. Our calculations also show that the improved sensitivity of the next-generation Very Large Array (ngVLA) is needed to probe the very low-density media characteristic of He stars that are the leading model for binary stellar companions of white dwarfs giving origin to Type Iax SNe.