Yes, if it is a qualified government debt the agency can request an offset of both your state and federal return.

For more information, see the TurboTax FAQ below

https://ttlc.intuit.com/replies/4143297

For Frequently Asked Questions on the Offset Program, please see the Treasury's link below.

https://fiscal.treasury.gov/fsservices/gov/debtColl/faqs/debt_questions_top_state.htm