LTD Benefit Payments

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Do I have to pay FICA tax on LTD benefit payments (from employer paid insurance) after 6 months from stopping work? 

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No, long-term disability insurance payments which you receive after 6 months' absence from work are not subject to Social security, Medicare and Futa taxes, if they are paid to you more than 6 calendar months after the last month in which you worked. 

Please refer to IRS Pub 15-A, Page 17.

The publication also shows two great examples supporting your situation.