The credit for the state taxes paid by the entity goes on the State return, as a payment.

(edit.... my comment applies to California.   Rick points out other states do it differently.)

It might help if you say which state.

There are generally two approaches, some states give a credit for the tax paid at the PTE level, other states exclude the income already taxed at the PTE level.  Either way *something* should probably flow through on a state-K1, where that gets entered I have no idea (and likely it depends on the state).