OK, I'm from Costa Rica so I can answer you with 100% certainty: It is not in North America and it is not in South America, it is in Central America.
Central America is called an isthmus, meaning that it joins two major geographical areas (North and South America).
Now, I must mention that in Costa Rica, we learn that there is only one American continent, which includes North America, Central America, and South America.
I know that in the U.S. you learn that North America and South America are two different continents, so I don't know where you leave Central America!
As you can see, the answer is different depending on where you are and what you are taught! Funny, huh?
I'd say that if you live in the U.S., you should find an elementary school geography book and see what it says about Central America.
But in Latin America, Costa Rica is in Central America. Period.