Refinance property tax

You deduct the entire amount that you paid in 2019, since that's the year in which you paid it. 

Possibly, but it depends.

You can deduct property tax that you pay to the government that applies to the period of time when you own the home. This includes amounts that you paid to the seller to reimburse the seller for previous property taxes, but it does not include amounts paid into escrow. Your escrow account is still your money until it is actually sent to the taxing authority.

for example, let’s assume that in your locality, the town property taxes cover the period from January 1 to December 31. The seller paid a full year in advance on January 1 of last year. If you bought the home in December, you paid the seller a few days worth of property tax to cover the last few days of December. That money is deductible as if you had paid it to the government.  If you also paid property taxes to the town to cover the January 2020 bill, they would also be deductible if you paid them in 2019.  But if you paid property tax money into an escrow account to be disbursed to the town later, it is still your money and you can’t deduct it until the property tax bill is actually paid by the escrow trustee.

likewise, if the city property taxes are billed on a July 1 to June 30 basis, then you probably paid the seller a credit for about six months worth of tax, to cover the December to June period that the seller already paid for, assuming the seller paid his taxes in July 2019.

In some states, property taxes are charged in arrears. The January 2020 tax bill would cover all of 2019.  In that case, the seller would pay to you at closing an amount equal to the taxes that would cover the period of time when they owned the home, and even though you paid the entire bill at the end of December, you could only deduct the few days worth when you were the owners.