I retired from LA State Government last year. I was required to pay my ex wife a one time payment of $34,587.73 from my DROP account. Is this amount tax deductable?

No, it would not be a tax deduction.  It would seem the Deferred Retirement Option Plan (DROP) would issue the ex wife a 1099-R for the distribution to her. If the payment was issued to you on a 1099-R you should check with the plan administrator to see if it should be issued to your ex wife.