State vs Federal Crime both have jurisdiction

Routh can be prosecuted on both federal and state charges. I do not see how the federal government can legally interfere with state investigation of a state crime. Even if convicted of Federal crime the state can still prosecute for the violation of state law. If convicted his state sentence could be served after his federal sentence is served. Or if by chance he is found not guilty in federal court, his state charges are still in play. Why would it not be illegal for the federal government to interfere with violation of Florida state law.