You may still be able to naturalize given the separation occurred after you filed for naturalization if you lived with your spouse for three years as a lawful permanent resident. You need to be honest at the interview when discussing the state of your marriage. You can read more about eligibility for naturalization at http://myattorneyusa.com/how-to-get-naturalized-in-the-united-states.
You would need to contact the local court with jurisdiction over divorce matters to see if a case has been initiated. You may also be able to locate the records in the court's website but this is not always an option.
Answered on Apr 14th, 2016 at 5:02 AM