Despite promising results from individual-level studies, state-level studies of the effectiveness of comprehensive background-check (CBC) policies in reducing firearm fatalities have yielded null results in multiple states. These prior studies focused on CBC laws adopted in the 1990s, when record keeping was far less complete. We estimated the effect of the implementation of CBC policies on state-level firearm homicide and suicide rates in states implementing CBC policies from 2013 to 2015 (Colorado, Delaware, Oregon, and Washington). We compared age-adjusted firearm homicide and suicide rates, measured annually from 15 years prior to policy implementation until 2019, in each treated state to rates in control groups constructed using the synthetic control group method. Differences in firearm homicide rates for Colorado, Oregon, and Washington post treatment were all small (0.09 to 0.18 per 100,000 residents per year) and not well distinguished from natural variation. Oregon had on average 0.80 per 100,000 fewer firearm suicides per year than did synthetic Oregon post treatment. However, these results were inconsistent across modeling approaches and not well distinguished from natural variation. Our models produced poor fit for Delaware. Coupled with previous null results from Indiana, California, Maryland, Pennsylvania, and Tennessee, the present results suggest that extending background check requirements to private transfers alone and implementing these policies as is currently done is not sufficient to achieve significant state-level reductions in firearm fatalities.