Costa Rica is not a United States territory, and there is no legal way to annex the country. It is a sovereign nation with its own government. It is not even contiguous with any other part of the United States. The majority of people in both nations would not support annexation.
While the U.S. has maintained a significant presence within the territory of Costa Rica, I believe they should not become a U.S. state if they do not decide so for themselves. This situation is reminscent of Hawaii in which the United States had no history with before takeover & eventual admission into the union. Costa Rica decides this for themselves every year, and every year they elect against admission.