Abstract Magneto-dielectric properties of (A²⁺)MnO₃-type perovskites are attractive for applications and stimulate extensive studies of these materials. Here, the complex dielectric and magnetic responses are investigated as in epitaxial films of SrTi₀.₆Mn₀.₄O₃, solid solution of paraelectric SrTiO₃ and magnetic SrMnO₃. The impedance and resonance measurements at frequencies of 10⁻²–10¹⁰ Hz and temperatures of 10–500 K reveal broad dielectric anomalies centered at 100–200 K, while the films are paramagnetic at all temperatures. Analysis shows polaronic electrical conductivity behind the observed behavior. Electron-phonon correlations, rather than spin-phonon correlations, are suggested to produce the apparent magneto-dielectric responses in many multiferroic manganites.