The main determinate is what state. There are over 40 state tax agencies, each doing its own thing. Some states are fairly quick with refunds, while other states (such as WV, WI, NC, GA, LA, AL, and others) can take a long time processing returns--even several weeks--as they crack down on detecting fraudulent returns. Of course, the Coronavirus situation may add to delays in some states. You may be able to get an idea about how long it takes in your state from the FAQs at your state's tax agency website as I will mention below.
Of course, folks need to be sure the state return was successfully filed. Since you didn't use TurboTax, our steps on how to check to see if was successfully efiled won't apply.
The FAQ below tells how to check on a state refund and has a link for your state.
TIP: While you're at your state's tax website, also look for a statement or FAQ that may say about how long it takes to get a refund in your state and how to long to wait before phoning the state tax agency. Many states have such information on their websites.
FAQ: How do I track my state refund?
https://ttlc.intuit.com/community/refund-status/help/how-do-i-track-my-state-refund/00/25571
