After you file

Each state will process the state tax return using different procedures, so that one state may be quicker in approving a state tax refund than another state.

 

See this TurboTax support FAQ for a New York state tax refund - https://ttlc.intuit.com/turbotax-support/en-us/help-article/tax-refund/track-new-york-tax-refund/L23...