If you and your spouse can come to a written agreement on how to divide the property taxes, then put the amount that you "paid" for on your return, and then be sure to keep the written agreement with your tax records in the unlikely chance that the IRS may write to ask about this. If your ex- deducts the other part of the property taxes, there should not be a problem.
Note that you can claim one half the property taxes only for that part of the year in which you were a co-owner.
However, you may want to see this: "If a divorce or separation agreement requires you or your spouse or former spouse to pay home mortgage interest on a home owned by both of you, the payment of interest may be alimony. See the discussion of Payments for jointly-owned home under Alimony in Pub. 504, Divorced or Separated Individuals. "
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