Upvote:2
If you are on one ticket, you bags can be checked through on international to international connections, meaning the airport supports/permits this.
However, you will need to confirm at check-in if this will happen.
If you do have to collect them, you just drop them off again right after exiting Customs. You do not need to go to the upper level counter.
Upvote:3
If it's on one ticket, your baggage will be checked through. However, in the US, you still need to collect it after passport control and take it through customs.
The difference is, if it's already tagged to Costa Rica, you can drop it off at the special drop-off before the exit into the public area, rather than having to take it to the ordinary bag drop desk