In many multitarget tracking applications in computer vision, a detection algorithm provides locations of potential targets. Subsequently, the measurements are associated with previously estimated target trajectories in a data association step. The output of the detector is often imperfect and the detection data may include multiple, split measurements from a single target or a single merged measurement from several targets. To address this problem, we introduce a multiple hypothesis tracker for interacting targets that generate split and merged measurements. The tracker is based on an efficient Markov chain Monte Carlo (MCMC) based auxiliary variable particle filter. The particle filter is Rao-Blackwellized such that the continuous target state parameters are estimated analytically, and an MCMC sampler generates samples from the large discrete space of data associations. In addition, we include experimental results in a scenario where we track several interacting targets that generate these split and merged measurements.