It depends. If LLC providing the Schedule K-1 operates and generates income in a state other than the member's residence, the member may need to report that income by filing a non-resident return in that state. Every state has its own requirements regarding income earned by nonresidents, so each member will need to investigate the filing requirements for that state and decide whether to file a state return.
Be sure to include sufficient information with the Schedule K-1 to allow reporting on a state return. You may need to review the requirements yourself to confirm the information is sufficient.
This article provides links to States with income tax: State Departments of Revenue