According to the New York State Department of Taxation and Finance:
New STAR applicants will receive a credit in the form of a check directly from NYS instead of receiving a school property tax exemption. The amount of your STAR benefit is the same regardless of how you receive it.
New Basic and Enhanced STAR applicants need to register with the NYS Department of Taxation and Finance to receive a STAR check. If you filed for the exemption with your local town assessor for the 2016 School Taxes (filing dates are between March 2, 2015 and March 1, 2016), you should have received notification from your town for the need to register for the Star Check through the NYS Department of Taxation and Finance.

Visit www.tax.ny.gov or call (518) 457-2036. Register by July 1 to receive your STAR check in September. If you register after July 1, you will receive your check later.
The eligibility criteria are the same for both the STAR credit and the STAR property tax exemption.
If you received a STAR exemption on your 2015 school tax bill, you will continue to receive the exemption and do not need to register for the STAR credit. You can also contact the Town of Marlborough Assessor’s Office at (845) 795-6167 Ext. 8 for assistance.