Department of Homeland Security (DHS) regulations required you to have your valid passport with you at all times. However, while traveling around the New Haven area, you should carry a copy of your I-94 record and your passport page with your biographic information and photo with you. Keep your passport in a secure location.
When traveling outside the New Haven area, carry your passport and immigration documents; they will be required for a domestic flight, but could also be requested on trips where you are traveling by car, train or bus. This is particularly relevant if you are traveling with two or three hours from the northern or southern U.S. borders. Your U.S. issued driver's license if generally not evidence of lawful status in the U.S.
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.