It's Feb 3rd. When will the AR1000NR form be ready? I can't finish filing until it gets updated.

Looks like 2/10 ... check the charts here :    https://ttlc.intuit.com/community/forms/help/state-forms-availability-table-for-turbotax-individual-personal-tax-products/00/26227

And you could file the federal now and the state later ... simply make that choice in the FILE tab. 

Form AR1000NR, Individual Income Tax Return Nonresident and Part-Year Resident for tax year 2021 is estimated to be finalized and available in TurboTax on 02/10/2022

Go to this TurboTax website for the Arkansas state forms availability - https://care-cdn.prodsupportsite.a.intuit.com/forms-availability/turbotax_ar_online_individual.html