Spatial diversity reception can be used over wireless optical links to mitigate atmospheric turbulence. Based on the clear atmospheric channel model and the model of diversity coherent receivers for laser communication, considering the spatial correlation of received signals, the error rates of both equal gain combining (EGC) and maximum ratio combining (MRC) are analyzed, and the outage probability of them are compared with that of selection combining (SC). The impact of spatial correlation of received signals on the diversity of coherent laser communication system is studied. The less spatial correlation of received signals is, the better the diversity reception for coherent free-space laser communication is. Simulations show that diversity can improve the performance of coherent laser communication. The performance of MRC is much better than those of EGC and SC, but SC is simpler and more convenient. Both performance and feasibility should be considered in applications.