All residency applications are governed by the Costa Rican Department of Immigration (Direccion General de Migracion y Extranjeria) which in turn is overseen by the Ministry of Public Security and Police (Ministerio de Gobernacion, Policia y Seguridad Publica).  Generally all applications for residency must be filed in your country of origin through the Costa Rican Consular Office in your area.  The only current exceptions are (1) Rentista and Pensionado Residency and (2) Immediate Relative Residency Petitions.  For list of Consular Offices in your area see the list on the Ministry of Foreign Relations site: Consular List.

Be advised that the residency procedures change from time to time.   In recent years Costa Rica has become an attractive destination for many and local officials have not been prepared to handle the influx.  As such,  due to internal changes in the Department of Immigration and severe under staffing there  are considerable delays in processing new applications.  Also, the approval of residency is a discretionary matter of the Department of Immigration.  The Department of Immigration favors applicants that can demonstrate that they will provide a financial benefit and contribute to create employment for Costa Rica citizens either in the form of direct investment (investors, enterpreneurs) or indirect investment (Rentista and Pensionados).