Deductions & credits

I also have similar situation as a buyer. I bought home and closed on Apr 30, 2021. In our county, the property taxes are paid for the previous year. They are running 12 months behind. The seller gave me a credit for Jul 1- Dec 31, 2020 and Jan-1 to Apr 30, 2021 period. In Aug 2021, I paid taxes for second half of 2020.

Is it correct that I cannot claim this on my state return becuase seller already credited me this.

 

On the other hand, for 2022 state tax return, I can claim only partial payment that I will be responsible (for the period of May 1 to Dec 31, 2021). Am I right?

 

The seller on the other hand will claim entire 2020 payments and partial (Jan-Apr 2021) tax payments on his tax return for his 2021 taxes. Can somebody please confirm? Thank you.