We study two multi-robot assignment problems for multi-target tracking. We consider distributed approaches in order to deal with limited sensing and communication ranges. We seek to simultaneously assign trajectories and targets to the robots. Our focus is on local algorithms that achieve performance close to the optimal algorithms with limited communication. We show how to use a local algorithm that guarantees a bounded approximate solution within $\mathcal{O}(h\log 1/\epsilon)$ communication rounds. We compare with a greedy approach that achieves a 2-approximation in as many rounds as the number of robots. Simulation results show that the local algorithm is an effective solution to the assignment problem.