Introducing a magnetic dopant into a topological insulator can give rise to ferromagnetic ordering which can break timereversal symmetry, realizing dissipationless electronic states in the absence of an external magnetic field. Assessment and control of the magnetic state can translate into novel future applications in quantum computing. We provide a detailed study of the magnetic state in Cr doped Sb<sub>2</sub>Te<sub>3</sub> thin films using terahertz time-domain spectroscopy (THz-TDS) and electrical transport. The temperature dependent behavior of the THz conductance of Cr<sub>x</sub>Sb<sub>2-x</sub>Te<sub>3</sub> thin films with <i>x</i> = 0.15 exhibits a clear insulator-metal transition at 40 K, indicating the onset of ferromagnetic order in the Cr<sub>x</sub>Sb<sub>2-x</sub>Te<sub>3</sub> at the TC (40 K). Moreover, the magneto-transport measurements showed anomalous Hall behavior below 40 K, demonstrating the consistency between the electrical and optical measurements. The direct correlation obtained between the carrier density and ferromagnetism in the magnetically doped topological insulators films, using the THz optical technique, strongly suggests a carrier-mediated RKKY coupling scenario. Our non-contact method of using THz radiation to investigate ferromagnetism and the consistency between optical and electrical measurements pave the way to realise exotic quantum states for spintronic and low energy magneto-electronic device applications.