Not necessarily. I don't know if a 1099-G is issued for a STAR check. In any case, you handle the STAR rebate differently on your tax return.
If you received a STAR check in 2016 for property taxes that you paid in 2016, it is not taxable income. Instead, reduce your property tax deduction by the amount of the check when filling out your deductions and credits. If you aren't deducting property taxes, then the STAR rebate is not income.
If you received a STAR check in 2016 for property taxes that you paid in 2015, then it is taxable "other income" but only if you took the itemized deduction and deducted property taxes on your 2015 return. If you deducted your 2015 taxes, then go to the other income section at the very bottom of the income page and indicate that you have a "taxable recovery" -- a reimbursement of a previous deduction, and enter the amount.
If you received a STAR check in 2017 for property taxes that you paid in 2016, the don't report it on your 2016 tax return. Instead, you will report it as "other income" on your 2017 tax return, but only if you take the itemized deduction and deduct property taxes on your 2016 return. You will go to the other income section at the very bottom of the income page and indicate that you have a "taxable recovery" -- a reimbursement of a previous deduction.
Whether or not the STAR check and the 1099-G are connected, the 1099-G represents taxable income that must be reported on your federal return.
Assuming, of course, that you filed Schedule A in 2015 and took a credit for real estate tax and state income tax.
Form 1099-G reports certain government payments, and the STAR tax refund would certainly qualify.
For more information, see the article below.