It depends. If the Schedule K-1 packet you received included additional information about states where the partnership operates and generates income, you may need to report that income by filing non-resident returns in those states. Every state has its own requirements regarding income earned by nonresidents, so you will need to investigate the filing requirements for that state and decide whether you should file a state return.
This article provides links to States with income tax: State Departments of Revenue
See the following article about filing a non-resident state return: