Your W-2 sounds correct. If you worked in New York all year, you owe tax to NY on all your wages because you worked in that state. So your employer will generally NOT withhold Connecticut tax because CT will give you a tax credit for tax paid to NY.
File a part-year NY tax return. Report all you income. Then file a part-year CT tax return and report the money you earned in NY while living in CT.
File a part-year CT tax return. In the Connecticut section look for Credit for Taxes Paid to Another State on the screen Take a look at Connecticut credit and taxes. Fill in the information to get a credit for your double taxed income.
