Recently, researchers conducted "a systematic review of 62 studies and 229 findings of police force size and crime from 1971 through 2013. Only studies of U.S. policing and containing standard errors of estimates were included." Their analysis revealed that, "the overall effect size for police force size on crime is negative, small, and not statistically significant."
The upshot of their meta-analysis: "This line of research has exhausted its utility. Changing policing strategy is likely to have a greater impact on crime than adding more police."
That's not what police chiefs and unions are telling city councils in local budget conversations. Regardless, at this point, the costs of adding ever-more officers without changing policing strategies and adequately funding various support services probably can't be justified in most instances.