You say "the university doesn't issue any tax documents related to the fellowship itself (e.g. no W-2, etc.)" then you say "the fellowship amount is listed on my 1098-T". If it's in box 5 of the 1098-T, that is a reporting tax document and that is how it is entered in TurboTax (TT). When TT sees that there is no offsetting tuition (in box 1), it will treat the box 5 amount as scholarship. It will show on line 1 of form 1040 with the notation SCH to the left. Anything on line 1 of the federal 1040 transfers to state.
What is your state? Most states tax scholarship (if the feds do), but some allow a deduction. You say " it looks like TurboTax populated the fellowship amount as a non-taxable scholarship in my State information". Where is that showing up.
