no you would not pay state tax on this, the premium in Box 13 is a reduction of income reported in Box 8 if you hold individual munis. if your munis are non-VA bonds then you will have an addition to income on your 760 Line 2 for the amount that is taxable which should be 1099-INT Box 8 less 1099-INT Box 13. Similarly your 1040 Line 2a should reflect the amount of muni income from 1099-INT, 1099-DIV, 1099-OID net of any premium or other adjustments.
(you should also be adjusting for any accrued interest paid when you purchased the bond, in the tax year of the first coupon, that is another reduction to Box 😎
the rub is when you have a mixture of VA and non-VA bonds though. after you enter the 1099-INT you will be asked how much of Box 8 comes from which state, but you can't specify how much of the premium is VA or non-VA. If you have a mixture of VA and non-VA bonds I have found it best to split up the 1099-INT and input the amounts from Box 8/13 (and any adjustment for accrued interest paid) for the VA bonds separately from the non-VA bonds, so you get the right amount of premium adjustment to the bonds that are taxable in VA.
hope that helps - feel free to reply if more questions.
