Do I used the Out of State Tax Credit Summary when reporting individual Nonresident Income tax information on a schedule k1 for Limited partnerships?

It depends. If you are required to file a nonresident state return for your K1, because your limited partnership is situated in a different state, then you could claim a credit for taxes paid to another state on your resident state return (assumes your state does have an income tax).

State Returns - Assumes both states require income tax returns to be filed: 

1. Report the income on each state return that is from the nonresident state
2. Report it on your resident state and receive credit for taxes paid to another state.

Credit for taxes paid to another state is allowed by a resident state when the same income is being taxed to another state.  Your resident state does not want you to pay tax twice on the same income. The credit that is allowed will be the lesser of:

1. the tax liability actually charged by the nonresident state, OR
2. the tax liability that would have been charged by your resident state

In most cases file your nonresident state first. This allows TurboTax to enter the credit on your resident state.