Single-cell analysis is used to gain insights into diseases, such as cancer. Advances in microfluidic solutions have enabled the efficient classification and analysis of a heterogeneous population of cells. Recently, a hybrid microfluidic platform was proposed for concurrent single-cell analysis on thousands of heterogeneous cells. In this design, barcoding droplets are routed using a valve-based routing fabric to label the input cells. However, prior work overlooked defects that are likely to occur during chip fabrication and system integration and the fault tolerance of this routing fabric remains a major concern. We address the above limitation and introduce a low-overhead design technique for guaranteeing the tolerance of single faults, while maintaining the efficiency of the cell-analysis platform. We show that the proposed method is optimal in that it minimizes the overhead in terms of fabric size.