Federal corruption laws only apply to federal politicians and employees. State corruption laws apply to state politicians, local and all such employees. All states have these laws, and are prosecuted, usually, under the State Attorney General's office.
The federal government has no role in such state matters, nor should it. Stae and federal laws differ, for a reason.
Very seldom ever happens, those in government who choose corruption are within a very clever safety net. All the states and the federal government have very carefully written immunity from prosecution laws keeping most political criminals in the green. Occasionally the U.S. or States Atty throws one of their own to the wolves to justify their existence and get votes next time around. In general they are all crooked as dog's legs.
When state and local officials are accused of corrupt activity, should they be prosecuted under federal laws by US attroneys
