Is there a way to adjust your state tax withholding by submitting a state-level equivalent of a W-4 Form?

Your withholding is completely based upon what you tell your employer. This is different in every state; however most states require your federal and state withholding to be the same, while others will automatically require a deduction based on your withholding (i.e. if you are married with no children you will have a withholding status of 2 dependents). In rare cases states will withhold for 1 dependant and only count you. I know this is hard to believe but the best tax return is $0.00; I know most people think it is best to receive money back; however no matter what you will be paying the taxes owed one way or another. So why treat the government as a savings account? You earn no interest by paying more taxes than necessary, ensure you have withholding justifiable to your household size, 1 per person that lives in your house.