Need state tax help

I usually file my state and federal taxes on my own using an online preparation software. I have really simple taxes where I always use the standard deduction and only have savings interest to add. This year I moved to a different state and I’ve completed my federal taxes, but I cannot for the life of me understand the tax law for the state that I moved to. And I’m not trusting what the software is telling me because it’s saying, I owe more taxes on only 1/3 the income for the entire year. Are there recommendations for cheap assistance for tax filing just for state?