Gun violence is a critical public safety concern in the United States. In 2006, California implemented a unique firearm monitoring program, the Armed and Prohibited Persons System (APPS), to address gun violence in the state. The APPS program first identifies those firearm owners who become prohibited from owning one, due to federal or state law, then confiscates their firearms. Our goal is to assess the effect of APPS on California murder rates using annual, state-level crime data across the U.S. for the years before and after the introduction of the program. To do so, we adapt a nonparametric Bayesian approach, multitask Gaussian processes (MTGPs), to the panel data setting. MTGPs allow for flexible and parsimonious panel data models that nest many existing approaches and allow for direct control over both dependence across time and dependence across units as well as natural uncertainty quantification. We extend this approach to incorporate non-Normal outcomes, auxiliary covariates, and multiple outcome series, which are all important in our application. We also show that this approach has attractive Frequentist properties, including a representation as a weighting estimator with separate weights over units and time periods. Applying this approach, we find that the increased monitoring and enforcement from the APPS program substantially decreased homicides in California. We also find that the effect on murder is driven entirely by declines in gun-related murder with no measurable effect on non-gun murder. Estimated cost per murder avoided are substantially lower than conventional estimates of the value of a statistical life, suggesting a very high benefit-cost ratio for this enforcement effort.