"Is there any way I can claim state tax exemption? "
I'm not sure what you are asking.
If the benefits were paid to you through the insurer, and the amount is reported in Box 14 and NOT included in Box 1, you are not being taxed on the benefits.
Why would you need an "exemption"?
If the benefits were paid by the state, you would have received a 1099-G and that would be taxable income.
Since your employer used a third party payer, you won't get a 1099-G from the state.
If your employer paid the premiums for that policy, the benefits would be included in Box 1 as wages of that employer's W-2.
If the benefits are only listed in Box 14 of the insurer's W-2, it isn't taxable.
@lviki
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