My official residence is Connecticut, but I also lived in NY from December through February, and since then I've been living in NJ. What residences do I put down?

[msoclof]

By 'official residence,' I mean the residence on my driver's license.

[TomD8]

Where was your main, permanent home as of 12/31/2019?  (Your state of residence for tax purposes is not determined by your drivers license.)

[msoclof]

In NY

[TomD8]

If your domicile was in New York at the end of 2019, then for purposes of your 2019 tax return, you would enter NY as your State of Residence in the personal info section of TT.

If you moved into NY from another state during 2019 (you changed your domicile to NY), or if you earned money in another state during 2019, also indicate those facts in the personal info section.

See this for the definition of domicile: https://www.tax.ny.gov/pit/file/pit_definitions.htm 

If you leave your domicile temporarily, for example to attend school in another state, and you intend to return, then your domicile does not change.