You are advised to carry your passport and immigration documents (your I-20, DS-2019 or I-797 form) with you when traveling in the U.S.; they will be required for a flight, but could also be requested on trips where you are traveling by car, train or bus. For more information about the documentation required for airtravel consult the guidelines of the Transportation Security Administation.
If you are traveling in and around the New Haven area carry a copy of your I-94 card, a copy of your I-20 Form, a copy of your passport page with your biographic information and photo with you at all times.
While it is extremely unlikely you would be questioned, having these documents with you provides immediate proof of your lawful status in the U.S. OISS can verify this information by phone should that ever be necessary.
Medex Travel Assistance Program
Traveling in the U.S.