An alternative to filing an amended return that may not make a difference in your tax liability would be to first add this income to your AGI from your filed return. Then see where the adjusted AGI would fall in the tax table. Use your filing status and the total income when you add the amount from the K-1 to check the Tax Table. If there is no change in what you would owe, then you do not need to amend your return.
2020 IRS Tax Table
For your second question about the state filing, here is the answer from GeoffreyG:
As such, you should know that it is common practice in the tax accounting community to simply "ignore" the state schedules for publicly-traded MLPs, unless the individual investor in question has a fairly large position in any one, specific, MLP. That is to avoid the (unnecessary and quite needless) filing of dozens of state tax returns that would otherwise result in no actual tax liability, or the payment of just a few dollars to any given state.
Thus, unless your particular MLP investment is valued at, say, more than several hundred-thousand dollars or so, then you can safely just ignore the state schedule(s) you received with your K-1 package, and focus your efforts instead on your federal K-1 data entry.
If you have a larger MLP investment than that, however, you probably should be using a professional tax preparation service anyway (CPA, Enrolled Agent, tax attorney), rather than doing it yourself through TurboTax, due to the higher level of technical difficulty involved.
This assumes that the amount of income is less than the minimum required for state filings.
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