I propose Robust Rao's Score (RS) test statistic to determine endogeneity of spatial weights matrices in a spatial dynamic panel data (SDPD) model (Qu, Lee, and Yu, 2017). I firstly introduce the bias-corrected score function since the score function is not centered around zero due to the two-way fixed effects. I further adjust score functions to rectify the over-rejection of the null hypothesis under a presence of local misspecification in contemporaneous dependence over space, dependence over time, or spatial time dependence. I then derive the explicit forms of our test statistic. A Monte Carlo simulation supports the analytics and shows nice finite sample properties. Finally, an empirical illustration is provided using data from Penn World Table version 6.1.