My mother is 87 and her only income is from social security. I have completed her federal return. Do i also need to complete a state return?

Depends on the state.  Some states tax SS others do not.  Which state do you live in?

She lives in North Carolina

North Carolina does not tax social security, so it is not necessary to prepare a state return.  Generally, if social security is her only income and there was no voluntary withholding a federal return is also not required.  

However, I know there are many folks who feel it is their duty to file anyway, and it's certainly okay to do so.

Thank you!