The IRS and state tax departments each maintain their own, separate tax collection systems.
This means you can't apply your federal refund to pay off your state taxes, nor the other way around.
https://ttlc.intuit.com/community/state-taxes/help/can-i-pay-my-state-taxes-from-my-federal-refund/0...
For more information about why your state refund was lower than you expected, check with your State Dept. of Revenue.
Here is help for contacting your State Department of Revenue:
https://ttlc.intuit.com/replies/3302452
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