My grandfather gifted me a house at the end of last year. He has paid all of the property tax and I don't live in it. Do I need to claim it on my return?

No you do not enter anything about the house on your tax return.  The recipient of a gift does not pay tax on the gift.  But Grandpa will need to look into filing a Form 709 gift tax form.

 

GIFTS

Money that you receive as a gift is not taxable income to you, and you do not need to report it on your income tax return.  Money that you gave as a gift to someone else is not deductible for your taxes.

 

Turbo Tax does not support the gift tax form 709, but here is a link:

https://www.irs.gov/pub/irs-pdf/f709.pdf

 

https://turbotax.intuit.com/tax-tips/estates/the-gift-tax-made-simple/L5tGWVC8N

 

https://www.forbes.com/sites/ashleaebeling/2017/10/19/irs-announces-2018-estate-and-gift-tax-limits-11-2-million-per-couple/#3226e75d4a4b

Why did he gift you a house? What do you use it for?  Is there a mortgage and who pays it? Who will pay the property tax in the future (including 2020)? Does grandpa have a "life estate" (the right to live there)?

 

Although you have nothing to report on your 2019 tax return, there are tax issues going forward.