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If you were legally married in Costa Rica, your marriage is considered to be legally valid in the U.S. Obtaining a divorce after a foreign marriage is not much different than terminating a marriage that occurred anywhere in the United States.
Assuming you meet the residency requirements to obtain a divorce in your particular state(usually ranging from 30 days to 6 months), you would need to obtain a petition for divorce (many states have blank forms online) and file it in the county where you live along with a filing fee which varies from one court to another. Since you don't know where your spouse lives, she would likely have to be served with the complaint by publication, which entails running a legal advertisement in the newspaper in the area where you think she lives or last lived. She will have a certain period of time in which to file an answer to your divorce petition after service is deemed to have been completed.
Your case will be set for a hearing, the judge will ask you a few questions, and then your divorce will be final.
Hope this helps. Good luck.
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