The Costa Rican banking system is quite different from what you are used to and 9/11 has changed it tremendously.
The US Government has obliged Costa Rican banks to make sure your money is legal and therefore they want to know everything about you. Since the banking system has been privatized, you can choose to open an account with different government owned banks (Public banks) or privately owned banks. Below are some useful links to help you.
Investor Manual : [Manual del Inversionista]
Coalition for Investment Initiatives (CINDE) : [Coalición Costarricense de Iniciativas de Desarrollo
Costa Rican-American Chamber of Commerce (AmCham)
Foreign Trade Promoter : [Promotora de Comercio Exterior]
Central Bank of Costa Rica (BCCR) : [Banco Central de Costa Rica]
National Bank of Costa Rica (BNCR) : [Banco Nacional]
Bank of Costa Rica (BCR) : [Banco de Costa Rica]
Bank of San Jose (BAC) : [Banco de San José]
Costa Rica Stock Exchange : [Bolsa Nacional de Valores S.A.]
Costa Rican Banking Association : [Asociación Bancaria Costarricense]
SUGEF (Regulating Organism for Financial Entities) : [Superintendencia General de Entidades Financieras]