The state tax that was withheld should have been included in the total state tax withheld on your 2020 state tax return. The state tax withheld should have been shown in box 14 of the 1099-R that you received for the 401(k) distribution. If it was shown in box 14, and the 1099-R was correctly entered in your 2020 tax return, then the state tax most likely was included on your state tax return. So you already got the $3,000 and it was applied to your 2020 state tax. There is nothing more for you to do.
If the total state tax withheld, including the $3,000 from the 401(k) withdrawal, was more than the total state tax that you had to pay for 2020, then you got a refund of the excess.
