Polarization‐dependent tip‐enhanced Raman spectroscopy (TERS) was carried out on double perovskite La2CoMnO6 (LCMO) thin films to determine the contributions of the enhancement by the excitation of surface plasmon polariton and tip‐induced polarization effects. Due to B‐site ordering and the resulting monoclinic P121/n1 structure, the spectra exhibit a strong Ag mode around 644 cm−1 originated from (Co/Mn)O6 stretching vibrations. The TERS contrast C, defined as the ratio of the total‐field (the sum of the near field and the far field) to the far‐field intensity, up to C ~60–110 for a cross‐polarized configuration (incident light polarization perpendicular to the detected one), reveals a possible breakdown of polarization‐dependent selection rules for the Raman scattering due to a tip‐induced near‐field depolarization component. We disentangled a significant enhancement for all observed modes in a parallel configuration with a TERS contrast of C ~2–5 due to general near‐field amplification, strongly affected also by the film thickness. With B‐site ordering and highly dielectric behavior, LCMO therefore provides an excellent test system to study TERS phenomena on oxide surfaces. Copyright © 2016 John Wiley & Sons, Ltd.