Structural, dielectric and magnetic properties of nano-size polycrystalline, La2CuMnO6 (LCM) samples were studied in the temperature range 80 K to 300 K. Orthorhombic single phase with space group 'Pnma' was confirmed by Rietveld refinement of XRD peaks. The small-polaron driven dielectric dispersion showed relaxation peaks in the vicinity of low-temperatures. The X-ray absorption spectroscopy (XAS) confirmed the charge states of Cu (2+) and Mn (4+) ions. DC-resistivity analysis supported the thermally activated conduction for high temperature and the variable range hoping (VRH) mechanism of conduction at low-temperature. The deviation of super-exchange angles between B-site cations from an ideal 180º value produced non-collinearity in the antiferromagnetic response of this ceramic and was confirmed canted antiferromagnetic behaviour. Positive Curie temperature along with finite coercivity indicated that the super-exchange interaction between Cu2+ and Mn4+ ions influenced the magnetic behaviour of this ceramics and showed a heterogenous magnetic response.