Connecticut has not issued guidance on the treatment of telecommuters. Your employer thinks you are subject to Connecticut income tax, which is why CT wages are listed on your W-2. I suggest filing a CT return.
I’m confused about what you mean by full-year New York wages since you said you lived and worked in PA. I’m assuming you mean you were telecommuting for a NY company while living and working in PA. That would explain why no PA tax was withheld, as you would receive credit on your PA return for tax paid to NY.
File a part-year PA return reporting the income you earned from NY while a resident of PA. You’ll have to manually figure the NY tax for PA tax credit. For example, if you earned $50,000 in PA and $100,000 total, you will use 50% (50k/100k) as the amount of NY tax eligible for credit. The tax rate for NY is much higher so you should not owe any money to PA, unless you have other PA income.
File a part-year NY tax return, but report your total NY income. Divide your NY income between NY income and NY source income. On New York Income Allocation, say Yes all you income was earned in NY state. Then enter the amount earned while a resident. Later you will see Tell us about your New York nonresident income. Enter the remaining amount. This should match the amount on your PA return as it represents the amount of NY income you earned while living in PA.
You can claim a credit for tax paid to CT. The NY program should pick this up automatically. You should get a refund for NY as you paying NY tax on CT income.
Last file a nonresident CT return and report the amount of income you earned while living in NY. You will owe CT income tax (since none was withheld). You should probably ask your employer to begin CT withholding for 2021.
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