The federal and state tax refunds come from different sources and on different schedules.
If accepted by the state use this TurboTax support FAQ to check the state tax refund status - https://ttlc.intuit.com/turbotax-support/en-us/help-article/tax-refund/track-state-refund/L3jgO8PGs_...
You can select your state on the website:
Check your State Refund.
You can also contact your state DOR
List of Department of Revenue by state List of state DOR's