As a student in NY, I live part time in the dorm. Residency is CT. When TT asks for address in NY, do I give my dorm address even though I have moved out by now?

For the address you enter in My Info, use the address you want the IRS to use if they need to send you a letter or a check.

No, you will give the address of where you live and receive your mail currently.  TurboTax is asking for your mailing address in the first steps.  

This part does not determine what taxes you file or anything else.  If your legal and permanent address is in CT, then you would use that address to file your taxes.

If you have received income while living as a student in NY, you will need to file both a NY and CT tax return.  Since NY is your non-resident state, you will file that one first, then the CT taking a tax credit for taxes paid to NY. 

You shouldn't have to enter a New York address. Where is TurboTax asking for that? In your New York tax return? When TurboTax asks "Did you maintain living quarters in New York State during 2022?" answer No. It doesn't mean a dorm room.

If it still asks you for a New York address, tell us the exact question in TurboTax, word for word, or post a screen shot of the question.

Yes  -  it's the part where TT asks about maintaining living quarters.  So Thanks a lot for your answer!!!