We report on the growth and magneto-electric (ME) coupling of Ca₃CoMnO₆ thin films deposited by pulsed laser deposition technique. Ca₃CoMnO₆ is interesting because of its tunable inter-chain magnetic interactions that affect its ME coupling. An optical band gap of 1.73eV was estimated by UV visible spectroscopy. The magnetic transition is surprisingly increased to 40K, much above its bulk value (15K). The increase in magnetic transition temperature is possibly due to stronger inter-chain interaction and strain caused by lattice mismatch. Due to canting the thin films show weak ferromagnetic like behavior at low temperature.The dielectric measurements show a nomaly at 10K and 40K which are clearly visible at the first derivative of dielectric data.From direct polarization measurements we associate the 10K transition to a magnetic structure driven ferroelectric phase. The magneto capacitance data at 5K shows substantial change in dielectric constant with magnetic field. The large ME coupling is also verified by polarization measurement, where a 5% change in polarization is observed on the application of 5 T external magnetic field.