Each K1 is going to look a little different so I would not be able to tell you a specific line item to look at. However, there should be a column that allocates income and adjustments to that state. Add up your income and your addbacks for each state and review the filing requirements for that state. Addbacks could be section 179 depreciation that is allowed on the federal return and not the state return.
Even if you are under the filing requirement, you would also file if you have withheld tax for that state. If you don't, you could leave potential refunds on the table. The cost of filing the state return should be less than the potential refund in this case.
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