High-temperature superconducting (HTS) coated conductors (CCs) have become the preferred material for superconducting magnet applications due to their high engineering current density and high mechanical strength. However, due to the low quench zone propagation velocity of CCs, magnets wound with CCs suffer from severe quench risks. Therefore, a rapid, sensitive, and reliable quench detection method is crucial for the safe operation of such HTS magnets. In this paper, we propose a quench detection method based on current redistribution, in which two pieces of HTS CCs are soldered together at each end and insulated in the middle part, which are then parallel co-wound into a double-pancake coil. The two tightly coupled windings and low resistance joints form a very low inductance current loop, resulting in fast current redistribution between the two co-windings even at the inception of quench (with still low quench voltage). We deduced analytical solutions of the current redistribution process under different magnet operational scenarios, including constant current operation, charging and discharging, and proposed quench detection criteria. Corresponding quench tests were performed on a small scale co-wound HTS coil, and the results well verified the analytical solutions and the effectiveness of the quench detection method. Our work may be useful for lowering the risks in HTS magnet quench in various applications.