You file a NY non-resident form (IT-203). You'l have to purchase the NY software from TurboTax (TT). TT will select the right form. Do the NY return first, then MA, so that TT can correctly calculate the credit.
Non resident instructions https://www.tax.ny.gov/pit/ads/it203_information.htm
For more on NY's notorious telecommuter tax, see http://www.journalofaccountancy.com/issues/2009/jun/20091371.html
If you work outside the state as a job requirement, you are only subject to New York State income tax on the days you work in New York. But if you work outside New York for your own convenience, you are subject to New York State income tax on all your income. Pennsylvania, Nebraska, Delaware and New Jersey have the same rule.
