it does make a difference.

any state tax withheld from a K-1 is entered on the K-1 input sheet.

In the case of Partnership it is entered on the Sch K-1 Partnership additional info 1

scroll down the page to Code W: Other deductions

Line 5  State income tax withheld               State Name        and amount

If there is more than one State with withholding, it requires a little more creativity but for one State it is easy.