No either way.
First, if you close in 2017, you won't have paid anything in 2016.
Second, when you close there is usually an adjustment on your closing statement for taxes that were prepaid by the previous owner. For example, if the previous owner paid property taxes in July for the period July 1, 2016 through June 30, 2017, and you buy the house in January, you will owe an adjustment credit to the seller for about half the year's taxes. (January through July) that the seller paid that apply to the period you will own the house. Those taxes are deductible on your 2017 tax return as if you paid them directly to the city or county. But you can't claim them on your 2016 tax return because you haven't paid them yet.
Even if the seller owes back taxes, and you end up paying property taxes for 2016 when you close in 2017, you can only take a deduction for the portion of property taxes that apply to when you owned the home. Taxes you pay that apply to when someone else owned the home are never deductible, but they are added to your cost basis (the price you paid) and may reduce your capital gains when you sell.
