Some taxpayers are exempted from paying the FICA tax. They canchoose not to have the federal income tax withheld from their paychecks. However, Medicare tax and Social Security tax will be deducted from their checks. Typically, you can claim an exemption if the following are true:  You received a refund of all your federal income tax that was withheld last year- as there was no tax liability on you.  You expect the same to happen this year as well.