In this study, we consider a pulse-Doppler radar relying on a simultaneously transmitting and reflecting reconfigurable intelligent surface (STAR-RIS) for scanning a given volume; the radar receiver is collocated with the STAR-RIS and aims to detect moving targets and estimate their radial velocity in the presence of clutter. To separate the echoes received from the transmissive and reflective half-spaces, the STAR-RIS superimposes a different slow-time modulation on the pulses redirected in each half-space, while the radar detector employs a decision rule based on a generalized information criterion (GIC). Two scanning policies are introduced, namely, simultaneous and sequential scanning, with different tradeoffs in terms of radial velocity estimation accuracy and complexity of the radar detector.