1) No. If the Schedule K-1 reports no income or expenses, you would not normally file a nonresident Massachusetts income tax return.
2) Yes. In the future, you will probably need to file a nonresident state return if the investment reports income or expenses on Schedule K-1.
From Massachusetts Personal Income Tax for Nonresidents:
If you're a nonresident of Massachusetts, you must file a Massachusetts Income Tax Return if you received Massachusetts source income [snip]. You're a nonresident if you are neither a full-year nor a part-year resident. Your Massachusetts tax treatment is based on your residency status and not the type of visa you hold.
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