Tax levied on income at the state level. State income taxes have their own set of deductions and credits that may be awarded for certain activities, such as contributing to a state-sponsored 529 plan. Taxpayers who itemized deductions on their federal returns may deduct state taxes paid on Schedule A. Not all states assess income tax. Alaska, Florida, Nevada, South Dakota, Texas, Washington and Wyoming have no state tax of any kind. New Hampshire and Tennessee levy tax on dividend and interest income only. Of course, the overall level of taxation varies from one state to another.