Fatal police shooting rates vary greatly across U.S. states, and states with higher firearm ownership rates tend to have higher rates of police shootings. Yet, despite well-documented national racial and ethnic disparities in fatal police shootings, prior research has not established how much these disparities vary across states, nor whether firearm ownership rates are associated with racial and ethnic disparities in police shootings. This article characterizes state-level fatal police shooting rates and racial/ethnic disparities in those rates, and tests whether firearm ownership rates are associated with these outcomes. Using 2015-2020 data on police shootings from the Washington Post, we predict fatal police shooting rates by state, year, and race/ethnicity using Bayesian multilevel count models. The degree of Black-White disparities in fatal police shooting rates varies by an order of magnitude across states, although Black rates exceed White rates in every state. In contrast, though Hispanic rates exceed White rates nationally, the opposite is true for 31 states. Southwestern states with large Hispanic-White disparities, relatively high shooting rates, and large Hispanic populations contribute most to the observed national disparity. Fatal police shooting rates are strongly associated with firearm ownership rates, but racial/ethnic disparities are either not related to firearm ownership rates or are larger in states with lower firearm ownership rates, depending on the group comparison and disparity metric. While state-level variation in firearm ownership may impact fatal police shooting rates, it is unlikely that higher firearm ownership rates explain why some states have such large racial/ethnic disparities compared to others.