Fill out Form 1040. Both Form 1040A and Form 1040 EZ only allow you to take a standard deduction and the inheritance tax is deducted as part of your itemized deductions. Unless the inheritance tax is the only major deduction you have, you need to be able to itemize your deductions on Schedule A, which comes with Form 1040. If the total of your deductions (including the inheritance tax) don't add up to more than the standard deduction ($5,950 for single filers and $11,900 for married filing jointly in 2012), then you save more by taking the standard deduction.
Calculate the total amount of tax paid to your state government associated with the inheritance.
Enter the amount on Schedule A. You will enter the amount of line 8, which is "Other taxes." You will also need to write that the amount is a state inheritance tax. This amount will be totaled up with all your other deductions and be used to reduce your taxable income. This, in turn, reduces the amount of federal income tax that you will owe.