The FBI is an organization under the Federal government. They may help with the state police and local police departments when a crime has occurred that is too big for the local police department to cover. In other words, when a local police department has a crime that needs more people or it needs more technology to solve and the local police department does not have access to that technology, then the FBI may assist.
In order for the FBI to come to the small city to help, the local or state police would have to notify them. Therefore, the FBI does have jurisdiction to interfere in the matters of the state police. However, they usually don’t interfere because they are meant to assist.