CAD problems for microfluidic biochips have recently gained much attention. One critical issue is the droplet routing problem. On cross-referencing biochips, the routing problem requires an efficient way to tackle the complexity of simultaneous droplet routing, scheduling and voltage assignment. In this paper, we present the first SAT based routing algorithm for droplet routing on cross-referencing biochips. The SAT-based technique solves a large problem size much more efficiently than a generic ILP formulation. We adopt a two-stage technique of global routing followed by detailed routing. In global routing, we iteratively route a set of nets that heavily interfere with each other. In detailed routing, we adopt a negotiation based routing algorithm and the droplet routing information obtained in the global routing stage is utilized for routing decision. The experimental results demonstrate the efficiency and effectiveness of the proposed SAT-based routing algorithm on a set of practical bioassays.