I think they can have jurisdiction of it pertains to federal elections
Right. I remember a vote-buying investigation in my home county in Alabama back in the 1970's where the sheriff was paying off voters with cash.
The FBI got involved because there were candidates for federal office (Senate, if I remember correctly) on the ballot. Ultimately, the sheriff did a few months of jail time. So although election procedures are normally the domain of the state, county or city, the feds can get involved related to federal office.
Here is a link to a lawsuit summary in the Appeals court related to this case, which gives good background in the first few paragraphs:
http://law.justia.com/cases/federal/appellate-courts/F2/615/329/415964/