After you file

Yes, the Federal and State tax refunds come separately.   Only the Federal refund goes through the intermediary bank.  The State tax refund goes directly from the State tax agency to you.

To check the Federal refund status:
<a rel="nofollow" target="_blank" href="http://www.irs.gov/Refunds">http://www.irs.gov/Refunds</a>

To check the New York State refund status:
<a rel="nofollow" target="_blank" href="https://ttlc.intuit.com/questions/2896795-how-do-i-track-my-new-york-tax-refund">https://ttlc.intuit...>