In this work, we investigate the performance of Rate-Splitting (RS) based on Tomlinson-Harashima Precoding (THP) in a multiple-antenna broadcast channel with perfect and imperfect Channel State Information at the Transmitter (CSIT). In particular, we consider RS using centralized and decentralized THP structures, where only one user splits its message into a common and private part, and develop expressions to describe the signal-to-interference-plus-noise (SINR) ratio and the sum rates associated with these schemes. Furthermore, we also assess the performance achieved by RS combined with Dirty-Paper Coding (DPC). Simulations show that RS with THP outperforms existing standard THP and RS with linear precoding schemes.