Cell-free (CF) systems have the potential to fulfill the increasing performance demand of future wireless applications by employing distributed access points (APs) that transmit the information over the same time-frequency resources. Due to the simultaneous transmission, multiuser interference (MUI) degrades the overall performance. To cope with the MUI in the downlink several linear precoding techniques, which rely on perfect channel state information at the transmitter (CSIT), have been studied. However, perfect CSIT is hardly obtained in practical systems. In this context, rate-splitting (RS) has arisen as a potential solution to deal with CSIT imperfections. In contrast to existing works, we explore non-linear precoding techniques along with RS-CF systems. Furthermore, the multi-branch (MB) concept is included to further enhance the overall performance of the system. Simulations show that the proposed MB-THP for RS-based CF systems outperforms the conventional linear precoders.