The answer to your question is that legally, yes, you do need to file a North Dakota state return, if you have any income from North Dakota sources and you are also filing a federal tax return. This is true whether you are a full-year resident, part-year resident, or nonresident of North Dakota.
Please see the following North Dakota Department of Revenue webpage for confirmation:
In particular, the FAQ titled "When is a nonresident of North Dakota required to file a North Dakota individual income tax return?" contains (in part) this quotation:
"A nonresident of North Dakota is required to file a North Dakota individual income tax return if the individual (1) is required to file a federal individual income tax for the tax year and (2) has any gross income from North Dakota sources."
To clarify, a partnership reporting flow-through income from North Dakota sources, via a K-1, is considered North Dakota source income.
That said, this is not to say that you actually owe anything (or much) from having just $20 in North Dakota income; but there remains a legal requirement to file a state tax return.
Because extra state tax returns cost money in TurboTax, and due to the simplicity of having just a single item of North Dakota income, you could attempt to complete the North Dakota return "off-line" and by hand, using the state's instructions and blank forms, which you can obtain for free. Such a state tax return could be printed and mailed outside of, and completely independent of, TurboTax. Everything you would need to accomplish this can be downloaded and printed from this North Dakota Office of Tax Commissioner webpage:
Thank you for asking this question.