Investigating Agency
The responding agency is going to be your city/county/state agency. So for example in Seattle that would be the Seattle Police Department, King County Sheriff's Office or Washington State Patrol. They will usually initiate the investiation too. If the crime also falls under federal purview, they may call the feds.
It is also possible that the feds will be working on a case and either work it alone until the end, or at some point invite another agency into the investigation.
Feds
Federal agents are rarely first responsders. You can read about the missions of the major federal law enforcement agencies through their links under the "Tips" tab of this website. If you need to have a fed working with a state or local officer in your story, consider a joint investigation or forming a task force with members from various agencies.
Interagency Squabble
This is a great place to add conflict to your story. Perhaps one agency is hiding something (not necessarily illegal), someone is perceived as slacking, one agency wants all the glory, or someone doesn't want to share some piece of information or evidence, etc.
The Perp
Do you want your criminal to be likeable? If so, do you really want him/her to be a criminal? And in case you're wondering...they ALL say they are innocent! :)