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.