In this study, we develop a holistic framework for space-time adaptive processing (STAP) in connected and automated vehicle (CAV) radar systems. We investigate a CAV system consisting of multiple vehicles that transmit frequency-modulated continuous-waveforms (FMCW), thereby functioning as a multistatic radar. Direct application of STAP in a network of radar systems such as in a CAV may lead to excess interference. We exploit time division multiplexing (TDM) to perform transmitter scheduling over FMCW pulses to achieve high detection performance. The TDM design problem is formulated as a quadratic assignment problem which is tackled by power method-like iterations and applying the Hungarian algorithm for linear assignment in each iteration. Numerical experiments confirm that the optimized TDM is successful in enhancing the target detection performance.