Tonight I will be leaving Recife, Brazil to go to Tucson, AZ, USA, with a stop in Rio and another stop in Houston. Will my checked-in baggage be directly delivered to Tucson after I leave it at a drop-off counter or will I have to check it in again at Houston?
Houston will be your first port of entry in the United States. As such, you will have to go through immigration and customs before you can board your flight to Tucson. Here's what you're likely to find:
- You'll get off the plane in Houston and walk down a series of corridors until you arrive at the immigration hall.
- You'll wait in line and go through immigration
- You'll go to the baggage claim for your flight and collect your checked luggage
- You'll take the luggage through customs (customs is often as simple as handing them your form and being waved through, unless they want to talk to you or look at your bags)
- You'll follow the signs for connecting flights, which will take you to a counter where they'll take your checked bags back. You can confirm they are tagged to go to Tucson at this time, if that didn't happen already for some reason. You can also ask the airline representatives here for directions to your gate.
- You'll continue through to TSA security before being allowed into the secure side of the terminal
Whenever you enter the USA, you need to go through immigration at the first airport, and there you must pick up your luggage and carry it through customs. Right behind customs, there will be agents of your airline and you can drop off your luggage with them again (and the airline will then transport it for as many legs as you fly).
If you don't do it, they will not send it after you (happened to multiple people I know already). Your luggage will sit in that airport until you go there and get it.
For your example, that means you need to do that in Houston.