The NTSB or similar will raise issue to the President
Okay, so Billy-Bob and his drinkin' buddy were out noodling for catfish when they — through the beer haze — see something come streaking down the sky and landing with a big, fat THUMP.
After going in to take a closer look (and — possible story element — picking up some scrap) they come to the highly qualified and expert conclusion that this is a thingy made of metal that dropped out of the sky... darned peculiar, but no matter, dealing with this thing is definitely above their pay grade (especially considering that their present profession is noodling for catfish).
So they call the Sheriff that — depending on smallness of their home town — they are probably well aquatinted with and give a slurred description of the event that — eventually — is interpreted to be a plane crash and that there are no survivors to deal with.
So the Sheriff starts up the normal procedures for dealing with a plane crash, this involves rescue services, paramedics to pick up the remains of people, the Federal Aviation Authority and the National Transportation Safety Board.
The FAA will within a few hours probably be very confused, as no planes — neither airlines nor general aviation — have been reported missing. Or(!)... maybe they have and this red herring adds to the plot line, when the supposedly missing plane is later found, somewhere else.
The NTSB will probably be site within anything from a few hours to a couple of days. Until then, the rescue services will have cordoned off the area to keep people from disturbing the site. Here you have flexility, so you can have people come as close or stay far away as you like.
As the NTSB gets on site, they will rather quickly realise that this is no aircraft, at least none that they are familiar with. This means that they will probably vacate the site, sharpish, since this could potentially be a very hazardous object. Hydrazine thrusters on rockets, or — worse — nuclear reactors / thermal isotope generators on satellites, or any number of other nasty components on space junk, are no laughing matter.
In any case, they will most likely conclude that this is a highly unusual event that require expertiese outside their domain. This means they will kick the issue up the chain of command. But since the NTSB is an independent authority, their parent agency is the Federal Government of the United States, meaning it lands in the lap of the President, right quick.
The President will then call together people to ask what should be done about this, such as...
- The Join Cheifs of Staff
- The Director of National Intelligence
- Various deparment heads of relevant agencues (see below)
...and start to issue orders to the various agencies under their command.
What happens next consists a large number of possibilities. It all depends on what other adminstrative agencies knew anything before this thing hit the ground, and which ones would have an interest in this thing.
Potential interested parties are...
18th Space Defense Squadron (18 SDS), located at Vandenburg Space Force Base in California, are reponsible for tracking objects in space, especially satellites. People will be asking them questions if any object is missing from their tracking catalog.
North American Aerospace Defense Command (NORAD) are responsible for providing aerospace early warning, and ditto protection. While they probably will not be involved once it is on the ground, people will be asking them some very serious questions on how something could fall from space without them sounding the big alert (because it could have been a hostile nuke)
Department of Homeland Security, since this thing is no longer flying — and thus no longer of interest to the FAA, NORAD, Air Force and other airspace related agencues — they will want to know what kind of threat it poses. And until it has been determined whether this unknown thing is a threat or not, they will probably act defensive and see it as a potential threat, and make sure no-one messes with it.
The Department of Energy (DoE) (for nuclear/radiological hazards), the Centers for Disease Control and Prevention (CDC) (biological) and the Environmental Protection Agency (EPA) (chemical) will probably be concerned already in the "We are not sure what it is" stage since — again — dangerous elements aboard this object might cause significant hazard to health and/or the environment. And when it becomes clear this is alien in origin, they will probably throw an utter [crap]-fit.
The tech-nerds at the Defense Advanced Research Projects Agency (DARPA) are equally going to have a fit, out of orgasmic delight.
"What about branches of the military?"
The military will not act on its own, but instead wait until told by the President to act. Why? Because this issue not a military threat, and it is not military property. The military cannot mount operations willy-nilly unless it is something that actually concerns them and their mission. While Hollywood loves to paint the military as this omnipotent entity that can do whatever they feel domestically, reality is that the military is tightly leashed in this area because an armed force running unchecked in the country is very dangerous.
"What about FBI, CIA, intelligence agencies?"
Again: this is outside their jurisdiction. An object falling out of space is not an intelligence issue, nor law enforcement issue, until someone has looked at it and concluded that this is the case. They might act, if the President calls them in, but they will not start acting on their own.
So, to summarise...
You have many options to branch your story how you want. But the initial agencies will most likely be...
- Local law enforcement and ditto rescue services
- The FAA and NTSB, which will kick the issue up the chain of command.
- The government and the President
- Whatever ad hoc task force the President puts together