Yes. Federal and state are completely separate and refunds come at different times from different places. A state refund comes directly from the state.
Make sure each return was accepted. You can check your efile status here <a rel="nofollow" target="_blank" href="
https://turbotax.intuit.com/tax-tools/efile-status-lookup/">https://turbotax.intuit.com/tax-tools/ef...>
