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You will reduce the amount of property tax you claim as paid on your Tax Year 2022 Federal Tax Return and here's why-

If you had already filed for 2022, you would need to calculate whether this rebate would have made your 2022 tax liability any different, and if yes, claim that difference as income for 2023. This would "recapture" the credit you already received. 

You would use the "State and Local Income Tax refund Worksheet" on page 84 of the 1040 instruction booklet. 

Since you have not yet filed, you would simply lower the tax you are claiming as paid in 2022 if you are itemizing. 

In essence this is the same as if you were calculating a credit recapture, but since you did not yet file, you would simply adjust for it on the current return, eliminating the need to recapture it in the following year's return. 

If for some reason, claiming income in the following year is more advantageous, I suppose a Taxpayer could do that and argue with the IRS if they questioned it.  

I should add that if you are not itemizing for 2022, the rebate has no effect on your tax liability and does not need to be addressed.  

Since it is a rebate, if you never claim the amount as a deduction, you never have to claim it as income or a credit recapture.

If Itemizing, the rebate would be handled in a similar way for your NY state return, although those instructions are not as clear.  They do refer to the credit as being received in the same tax year, but I believe the intent is to match the credit to the tax year in which the property tax paid was/is being claimed as a deduction. 

IRS Pub 530 states: page 4

"Refund or rebate of real estate taxes. If you receive a refund or rebate of real estate taxes this year for amounts you paid this year, you must reduce your real estate tax deduction by the amount refunded to you. If the refund or rebate was for real estate taxes paid for a prior year, you may have to include some or all of the refund in your income. For more information, see Recoveries in Pub. 525, Taxable and Nontaxable Income."

IRS Pub 525 states: page 25

“…, use the State and Local Income Tax Refund Worksheet—Schedule 1, Line 1, in the 2022 Instructions for Schedule 1 (Form 1040) for line 1 to figure the amount (if any) to include in your income. See the Instructions for Forms 1040 and 1040-SR.”

NY Homeowner tax rebate

"If you receive a check for the homeowner tax rebate credit, you do not need to do anything on your New York State income tax return unless you itemize your deductions."

NY How to Report Tax Credit Rebate

“If you itemize your deductions, reduce your itemized deduction for real estate taxes paid by the total amount of any STAR credit and the homeowner tax rebate credit received during the tax year; keep your check stubs with your tax records.”