Having a dependent does affect your state income taxes, but often less than it affects federal taxes. Most states will cut your taxes in various ways if you have a dependent, but with smaller tax breaks than you get from the feds. In some states, dependents make no difference: Florida, for example, doesn't have a state income tax.
States defer to the federal rules for defining who your dependents are. A dependent can be either a qualifying child or a qualifying relative. Qualifying children can include your children, stepchildren, and foster children, as well as younger siblings and their children who meet certain guidelines. Qualifying relatives can include any other person -- even someone like a boyfriend or girlfriend -- who meets the complex IRS rules for relying on you for financial support. In most cases, you must provide more than half your dependents' support, and they must usually live with you.
The personal exemption for dependents varies from state to state. For the 2012 tax year, for example, the federal exemption is $3,800 but New Jersey only allows $1,500. These exemptions represent deductions from income, meaning that you don't pay tax on that amount of income. In Iowa the exemption credit is only $40 -- but it's a credit, not a deduction, meaning that it reduces your tax bill dollar-for-dollar.
Your state department of revenue can tell you whether your state grants you any particular tax credits for dependents. North Carolina, for example, allows you to take a child-care credit, which is based on a percentage of your expenses. The maximum you can receive is $390 for one child, or $780 for two or more children. Like the federal credit, you qualify by paying for child care so that you and your spouse can work or look for work.
Federal tax law changes constantly, year to year. State taxes change too, but not always at the same rate. Under the federal Affordable Care Act, for example, if your workplace health insurance covers health-care for a qualifying child, it isn't a taxable fringe benefit. States whose tax laws are based on older versions of federal law still treat the cost of buying the child's insurance as taxable coverage. Never assume changes to federal tax law applies at the state level until you've checked with your department of revenue.
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