Your state will tax 401(k) withdrawals as ordinary income, there is no additional penalty or special tax at the state level. So it depends on your state and your other income. It could be a low as 3-4% or as high as 13% in California.
You can try looking up your state tax brackets here. Add up all your taxable income including the amount of the 401(k) withdrawal and look at the top tax bracket for your income and marital status; your withdrawal will be taxed at that top rate.
https://taxfoundation.org/state-individual-income-tax-rates-and-brackets-for-2020/