You should always disclose to your immigration lawyer whether you can be construed to be married to more than one person.
This is one of those areas of immigration law (like adultery having caused the breakup of a pre-existing marriage) where, although you may be able to successfully apply for a Green Card, the guidance is clear that you would be precluded from gaining citizenship if the polygamous act was committed during the statutory 5 year period for purposes of naturalization.
The INA defines Polygamy as “the custom of having more than one spouse at the same time.” Immigration Officers are directed to review documents in the applicant’s file and any documents the applicant brings to the interview for information about the applicant’s marital history, to include any visa petitions or applications, marriage and divorce certificates, and birth certificates of children. See INA 101(f)(3) and INA 212(a)(10)(A). See 8 CFR 316.10(b)(2)(ix).
Note that Polygamy is not the same as bigamy. Bigamy is the crime of marrying a person while being legally married to someone else. An applicant who has committed bigamy may be susceptible to a denial under the “unlawful acts” provision.
Additionally, not disclosing your complete marital history in Immigration Court can have fatal consequences if you are in deportation court.
The Immigration Judge denied voluntary departure on the ground that the respondent knew that there was an impediment to his adjustment of status in 1985 (i.e., his prior undisclosed marriage) and continued to maintain the deception for many years. Although the Immigration Judge stated at the hearing that he would entertain a motion to reopen to allow the respondent to apply for cancellation of removal under section 240A(b) of the Act, he indicated that he would likely find the respondent ineligible for th at relief as well, based on his lack of good moral character. We do not construe this statement as precluding the respondent from applying for such relief. We note, however, that there is a separate question whether, as a result of his misrepresentation and bigamy, the respondent is barred from establishing eligibility by the stop-time provisions of section 240A(d)(1)(B), which relate to the commission of certain offenses, including crimes involving moral turpitude. In the event the Immigration Judge finds the respondent eligible for cancellation of removal under section 240A(b), he may also wish to reconsider his denial of voluntary departure.
If you go all the way back to the first iteration of Federal Immigration Law, the intent has always been to prevent polygamous FNs (the Chinese back then) from gaining status in the US as a public policy. Here’s an ICE authored article on the topic: https://www.justice.gov/sites/default/files/civil/legacy/2014/10/17/October_2012.pdf
It is always extremely important to note that a divorce in your home country may not be valid in the U.S. See https://www.uscis.gov/sites/default/files/err/H2%20-%20Waiver%20of%20Inadmissibility%20-%20Criminal%20-%20212%20(h)/Decisions_Issued_in_2014/DEC182014_01H2212.pdf
If, for example, you divorce your Filipino Spouse in the U.S. and subsequently remarry a U.S. Citizen in the United States, you may be deemed ineligible to apply for a Green Card for having committed the crime of Bigamy.
You can see that disclosing your complete marital and divorce history to your attorney before your attorney files your Green Card or Citizenship Application is of the utmost importance.