New York has step-by-step instructions for completing Form IT-2104 here:
Instructions for Form IT-2104 (ny.gov)
Your Line 1 allowances will be determined by the worksheet in the instructions. You will have zero allowances on Line 2, since you are not a resident of NYC. (I am assuming you will NOT maintain a place of abode in NYC and spend 184 days or more in NYC.)
Since you are a non-resident of NY whose assigned office is within NY, and you will be performing some work remotely from a location outside NY, you will be subject to NY's "convenience of the employer" rule. This means that, unless you are required or assigned by your employer to work from a location outside NY, the income you earn by working remotely will be considered "New York source" income and thus taxable by New York. You can read the details of the "convenience" rule here:
https://www.tax.ny.gov/pdf/memos/income/m06_5i.pdf
The "if applicable" phrase in line 1 means "and Yonkers, if applicable".
ALL your income, including your New York earnings, will be taxable by your home state of CT. But CT will give you an "other state credit" for the taxes you pay to NY. The credit prevents double taxation, which is prohibited by federal law. At tax time you will be filing both a non-resident NY tax return and your home state CT tax return. Using TurboTax, you'll file the non-resident NY return before you do the home state CT return. The program will then calculate and apply the "other state credit."
**Answers are correct to the best of my ability but do not constitute tax or legal advice.
