Can I omit a previous address from my tax return info? (NY)?

NY City income tax applies only during the period while you are a city resident. If you were a city resident for only part of the year, you must submit Form IT-360.1 with your NY State income tax filing. Thus, you must report your move out of the city, whether it benefits you or not. It would be tax fraud to claim you never lived in the city, and it would cost you extra tax to claim you lived in the city for the whole year.

You are required to tell them. Telling the truth benefits you, because the punishment if you don't could be much more than the tax.

No you cannot omit your previous address without putting yourself in danger for an audit and/or possible tax fraud.

You can do whatever you like. Your taxes will be wrong and you will run the risk of getting audited and subjected to fines.

If you were in the city for 183 days or more (working or residing) you are considered a NYC resident. If your job was outside the city (didn't withhold city taxes) and you moved before July 1, then you are a part-year resident and would answer the moving question "yes".