It depends on what you put on your refugee application. My guess would be iraq. It would be best to consult an immigration attorney.
Alexus P. Sham firstname.lastname@example.org (917) 498-9009. The above information is only general in nature and does not constitute legal advice. It does not create an attorney-client relationship.
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(213) 394-4554 x0 Mr. Shusterman is a former INS Trial Attorney (1976-82) with over 35 years of immigration experience. His response to your question is general in nature, as not all the facts are known to him. You should retain an attorney experienced in immigration law to review all the facts in your case in order to receive advice specific to your case. Mr. Shusterman's statement above does not create an attorney/client relationship.
The question refers to the country you would need refuge from, so probably Iraq.
You may want to get some advice before you travel, especially if you do not have your green card yet, so you are fully prepared for your trip and do not put your status at risk. If money is an issue, you could always check with your resettlement agency for information and/or an agency offering immigration legal services, like some Catholic Charities, local area legal aid organizations, etc.