If I live in one state but work in another. Is it normal to receive a refund in my resident state and still owe taxes to my work state?

[Mike9241]

Yes. What states?  Some states have reciprocity which means wages are taxed only by your resident state.  You might need to file two state returns if there is. A nonresident state return to get back any withholding for that state; no withholding - no filing unless you earned other income in that state. A resident state return to pay taxes on all wages earned in the other state. Another key factor is to do the nonresident state first.  if there is no reciprocity, your resident state uses the tax likability (not the taxes paid) to compute a tax credit to minimize or eliminate the double taxation.  

[Hal_Al]

Yes. 

This is the general rule: The income is work state (WS) source income since it was earned there. Resident States (RS) tax all their resident's income, regardless of where earned. You will file a non-resident tax return for the WS and report the WS income. You will file a full year resident return for the RS, reporting all your income. The RS will give you a credit, or partial credit for any tax paid to the WS.

Some states have reciprocal agreements, on wages, with  neighboring states. No WS state taxes are withheld or due and you do not need to file a WS return. But your home state will tax you on your WS income.

. In a reciprocal situation, the RS will not give you a credit for tax paid to the WS. Instead, if WS taxes are mistakenly withheld, you have to file a WS return to get a refund.

https://ttlc.intuit.com/turbotax-support/en-us/help-article/state-taxes/states-reciprocal-agreements...