My employer is in Vermont and I live in NY. Do I file the state tax for NY or Vermont? The W2 shows that taxes are deducted for VT state. Please help !What do I do?

Where do you actually perform the work?

Work is performed in New York.

OK ... step 1 ... talk to the employer to stop the VT withholding since you live & work in NY... and see if they will withhold NY taxes instead. 

step 2 ... in the MY INFO section you will only enter that you live & work in NY

step 3 ... in the STATE tab you will file a resident NY return and a NON resident VT return and allocate nothing to VT so you get all the withholding  back. 

Assuming you actually work in VT, see this:

http://tax.vermont.gov/individuals/income-tax-returns/who-needs-to-file/nonresident

You will then file a resident return in NY, and get credit for most or all of the taxes paid to VT. But you may still owe NY some money, due to the difference in tax rates between the two states, or if you have other, nonwage income.

Thank you  for the response! The work is actually performed in New York.

@SweetieJean,  states that allow credits for double-taxed income generally calculate in some form using the tax liability in the other stare.  since he has no double-taxed income, NY will probably not allow any credit for the VT taxes.  Why should NY allow a credirt when he's getting back all his VT withholdings.

My answer assumed he works in VT, but he doesn't.

Unfortunately, I never got any of my VT tax withholdings. How to go about with getting the VT withholdings back?

File a nonresident tax return in VT.