Most states have income taxes that feature varying levels of conformity with the Federal rules.
For example, the tax liability in California is calculated similarly to the Federal. There are some differences that change every year. The tax rate on net taxable income varies from 0% to 12.3%. For the income in excess of $1,000,000 per year, there is an extra 1% of the mental health services tax.
The following states in the U.S. do not have income taxes: Alaska, Florida, Nevada, New Hampshire, South Dakota, Tennessee, Texas, Washington, and Wyoming.