State Income Tax is only deductible on a Federal Income Tax Return as an itemized deduction. If you take the standard deduction you will get no benefit on your federal tax return from paying a state income tax.  Most middle income people only itemize deductions when they are paying significant mortgage interest.  Renters and those who own their homes or have almost paid their mortgage usually don't itemize because the standard deduction is greater. 


This is from the IRS website: https://www.irs.gov/taxtopics/tc503.html
Topic 503 - Deductible Taxes
There are four types of deductible non business taxes:State, local, and foreign income taxes; State and local general sales taxes;State, local, and foreign real estate taxes, and State and local personal property taxes
To be deductible, the tax must be imposed on you and you must have paid it during your tax year. Taxes may be claimed only as an itemized deduction on Form 1040, Schedule A (PDF), Itemized Deductions.