You will get your certificate at the oath ceremony usually scheduled 2 months after the interview - sometimes faster.
You can petition your parents after your certificate is in your hand. Not before. No need to wait for the passport.
as far as getting sworn in - depends on the jurisdiction. For example, Newark NJ does same day ceremonies, but not in NY.
Filing for parents - you can do so as soon as you get the certificate, no need to wait for passport
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Some states like New Jersey have same day oath ceremonies where you receive your certificate of naturalization the same day. However most states the oath ceremony takes place a few weeks to a couple of months later. Once you have your certificate of naturalization you can petition/apply for a green card for your parents and do not need to wait for a US passport.
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You will get the "Certificate of Naturalization" on the day you take the oath of citizenship at the oath ceremony. You don't have to wait for US passport to file a petition on behalf of your parents. Congratulations and good luck.
I agree with my colleagues.
If you have additional questions, you can always contact an immigration lawyer, whether myself or one of my colleagues. If you appreciate the time spent preparing this answer, kindly consider marking it HELPFUL. Good luck to you.
Dean P. Murray
The Murray Law Firm
560 Sylvan Avenue
Englewood Cliffs, NJ 07632
Mr. Murray's response is NOT legal advice and does NOT create an attorney-client relationship. You should NOT rely on this response. Mr. Murray's response was generated without conducting a full inquiry as would occur during a face to face attorney-client consultation. It is likely that the response above may be made less accurate, or become entirely inaccurate, as you, i.e. the questioner, disclose additional facts that should only be discussed during a private consultation with an attorney. I strongly recommend that you consult an attorney who is licensed to practice law in your state (or, in the case of immigration law, and attorney in ANY state), whereupon all relevant facts will be discussed. All responses posted by Mr. Murray on Avvo.com are intended as general information for the education of the public, and not for any specific individual.
I agree with my colleagues - you don't have to wait for your passport to file for your parents. If your citizenship interview is in Fairfax, VA (if you live in Woodbridge that will be the case) you will not get your certificate on the same day.
Here are some additional hints about your interview that you might find useful. When you get your interview notice, it will include a list of documents to bring to the interview. Frequently at the interview, however, they will ask for things that are not on that list. For example, if you admit to traffic violations, you should have proof you paid the fines, particularly if you have admitted to a lot of violations. In addition, lately a lot of interviewers have been asking to see birth certificates, so have yours ready. Finally, be sure to bring a couple of pieces of correspondence that have your current address - they may want to see proof that you are still living in their jurisdiction. If you would like more information check out my website at www.marklawimmigrant.com. Good luck at your interview.
This response does not create an attorney client relationship and is for informational purposes only. Before acting on this information you should discuss your problem with an immigration attorney.