I got a state tax assessment on a prior year tax return that I filed through turbo tax. How can I get help verifying that it's accurate and/or refuting it with the state?

It all depends on where you lived and where you worked during the year.  

Scenario 1: You lived in DE but worked in MD:  In this case, you would pay state taxes to MD on the income you earned there..  You should have filed a non-resident MD return and on your resident DE return, you should have received a credit for the taxes that you paid to MD.

Scenario 2: : You lived in MD but worked in DE:  In this case, you would pay state taxes to DE on the income you earned there.  You should have filed a non-resident DE return and on your resident MD return, you should have received a credit for the taxes that you paid to DE.

You may need to amend your MD & DE tax returns if they were not prepared using the guidelines above.