The process of applying for a green card (U.S. lawful permanent residence) requires applicants to submit various documents regarding their personal background. For example, if you are applying for adjustment of status in the United States based on a family relationship, you will need to submit copies of your birth certificate and evidence of family relationships such as marriage and divorce certificates. If you are applying for a family-based immigrant visa from outside the United States (through consular processing), you will be required to submit not only original or certified copies of your birth certificate, marriage certificate (if applicable), and divorce certificate (if applicable), but also police records from every country you resided in for more than one year, prison records (if applicable), and military records (if applicable).
If you don't have one of the needed documents in your possession, then U.S. immigration authorities expect you to contact the appropriate government agency for a replacement. However, some applicants are not able to secure all of the necessary documents for the green card process because they are simply not available in their home country.
If you find that you are unable to secure one of documents required for your green card, the first thing you will need to do is confirm that the document is really not available. You can do this by visiting the U.S. Department of State (DOS) Country Reciprocity and Civil Documents by Country page. Select your home country then, when its page comes up, scroll down to review the “Documents” section. This includes a heading for each required document for the green card process and states whether or not it is available.
If your document is available, you must follow the guidance provided on how to obtain it. If the document is unavailable despite the DOS thinking it is available, your best bet is to request proof of this, in the form of a certificate of non-availability from the appropriate governmental authority.
If a document is listed as available but you are having difficulty securing it, or a certificate of non-availability, from the appropriate governmental authority, you might be able to separately show that the document is “unobtainable.” In order to do that, you will have to demonstrate that securing the document will cause you or your family member hardship that is beyond a normal delay or inconvenience. You will need to provide evidence of the efforts you made to secure the document, as well as the hardship that will result if you are forced to obtain it.
If, even after your best efforts, a document is truly not available, or has otherwise been deemed unobtainable, you must submit secondary evidence of the family relationship (or other thing that you're trying to prove) in addition to a certificate of non-availability. See the Country Reciprocity Table for any guidance it might offer on what type of secondary evidence will suffice for the document you are missing.
Commonly accepted forms of secondary evidence include, but are not limited to:
Immigration applications and the associated USCIS bureaucracy can be intimidating to even the most well-informed applicants. An immigration attorney can provide you with assistance if you are having difficulty obtaining an available document, or obtaining secondary evidence for a document that is not available. For example, the attorney might be able to interview your parents and help draft an affidavit in their words, on their behalf. See this survey on Family-Based Green Cards: Are Immigration Lawyers Worth the Cost?.