Phasor measurement units (PMU) provide time-synchronized linear measurements for power system state estimation. In practice, the synchronization is not perfect for various reasons. In this paper we derive the posterior Cramér-Rao bound on the estimation error based on a realistic measurement model which takes into account the synchronization error. We then use a greedy algorithm for PMU placement based on the derived bound, and compare the results with other heuristics and the optimal solution through exhaustive search. Numerical examples demonstrate the performance improvement using the PMU placement profile from the greedy algorithm. The results also indicate that the greedy technique closely approximates the optimal solution.