I live in NYS and I moved in 2020 (still in NYS) for personal reasons. Can I deduct my moving expenses?

It depends.

Moving expenses are no longer a deductible item on your federal return unless you meet certain exceptions.  See the following link for more details.  

Moving expenses

However, you can deduct them on your New York state return. Please follow the instructions below to enter them into the TurboTax program.  

Go to the Federal interview section in the black panel on the left. 

1. Select Deductions & Credits 
2. Select All tax breaks and scroll down until you see Other Deductions and Credits 
3. Select Moving Expenses 
4. Proceed to go through the screens and enter the information as applicable 

The deduction will not apply on the federal return but your input here will flow into your New York state income tax return.