Suggest that you get the official tax map number of the parcel that you are interested in; generally you can get that by a visit to the tax assessors department at the village or town hall where that property is located. Also most brokers maintain local tax map records. Then, have your real estate broker put in a call to the tax assessors office with that exact map number and the saff usually will answer that inquiry or at least will tell you how to get the answer. In my opinion I would start with the tax map number if I were you.
Call the Town of Islip Assessor's office 631-224-5585 to get item number. Then call 631-224-5580 with the item number. They will not give you the STAR reduction. STAR number is 631-224-5058. If you are calling about East Islip, STAR is $968.
Your tax assessor in Brooklyn has a website online where you can look up any property by owner or by tax ID number. If you need assistance though, your Realtor can look up the information easily on the local MLS system. You could also call the Tax Assessor's office for the information if it is new and not yet posted.