In the US it's a mix. Quoting from a recent post[1] on a law professor blog regarding the relationship between the states and the federal government on crimina

In the US it's a mix. Quoting from a recent post[1] on a law professor blog regarding the relationship between the states and the federal government on criminal matters: "...[T]he states and the federal government are not exactly co-equals in the criminal law sphere. The states have general police powers while the federal government has limited powers; the states inherited the common law while the federal government must enact statutory offenses." [1] http://www.volokh.com/2012/08/03/can-federal-border-patrol-agents-pull-over-cars-based-only-on-state-traffic-law-violations/ http://www.volokh.com/2012/08/03/can-federal-border-patrol-a...