A method for the design, construction, and assembly of modular, polymer-based, microfluidic devices using simple micro-assembly technology was demonstrated to build an integrated fluidic system consisting of vertically stacked modules for carrying out multi-step molecular assays. As an example of the utility of the modular system, point mutation detection using the ligase detection reaction (LDR) following amplification by the polymerase chain reaction (PCR) was carried out. Fluid interconnects and standoffs ensured that temperatures in the vertically stacked reactors were within ± 0.2 C° at the center of the temperature zones and ± 1.1 C° overall. The vertical spacing between modules was confirmed using finite element models (ANSYS, Inc., Canonsburg, PA) to simulate the steady-state temperature distribution for the assembly. Passive alignment structures, including a hemispherical pin-in-hole, a hemispherical pin-in-slot, and a plate-plate lap joint, were developed using screw theory to enable accurate exactly constrained assembly of the microfluidic reactors, cover sheets, and fluid interconnects to facilitate the modular approach. The mean mismatch between the centers of adjacent through holes was 64 ± 7.7 μm, significantly reducing the dead volume necessary to accommodate manufacturing variation. The microfluidic components were easily assembled by hand and the assembly of several different configurations of microfluidic modules for executing the assay was evaluated. Temperatures were measured in the desired range in each reactor. The biochemical performance was comparable to that obtained with benchtop instruments, but took less than 45 min to execute, half the time.