The title of this post is misleading: should be something like "Investigation of a potential crime committed by a Federal Officer is done by federal agencies first. Other (state, local, etc.) agencies may investigate later."

The implication of the original title is that no investigation whatsoever is possible if a federal officer commits a potential crime. That is clearly false.

The law simply provides a time priority for investigations, something much=needed especially when the various agencies involved have competing (and, in this case, political) goals in their investigations.