Contact your home State MV agency, and confirm that there are no issues regarding your license. If the NY State authorities had notified your home State of the failure to appear, your license would most likely be suspended. If the license is in good shape, use it to get a new license issued in CT.
As to checking on the status of the NY charge, contact the NYC Court where the summons was issued. If you give them your identifiers they should be able to pull up the case and tell you the status. If a warrant was issued, ask for the bail amount and send it in, which will lift the warrant and give you a new Court date. I suggest you discuss the possible options to actually dispose of the case with a criminal defense lawyer before you go to Court, if it is in fact still open. Good luck.
This answer does not create an attorney-client relationship or constitute legal advice. Instead, given the nature of this website, it is provided solely for informational purposes, for you to use as a starting point when speaking directly with a lawyer in your State. Do not assume that the legal theories I mention that pertain to NJ will apply in your State. The laws of each State; and, the facts of each case are different, and it is therefore critical for you to consult with a lawyer admitted to practice law in your State before making any decisions on how to handle or dispose of your case.