It depends. If the income reported on Schedule K-1 for a state exceeds the minimum to file for that state, you will need to file a non-resident State Income Tax return (in addition to your home state). If you find that you must file non-resident state returns, complete all of them first before you begin your resident state return. This allows TurboTax to apply credits for taxes paid to other states.
This post has links to the filing requirements for those states that have income tax: Do I need to file a state return?