The experimental discovery of the fractionalized Hall conductivity revealed new types of quantum particles beyond bosons and fermions. These anyons are usually studied deep inside a topological phase. But can such fractionalization be detected at the phase transition point to a conventional phase? To answer this question, we study a quantum phase transition between a topological state called a Z_2 spin liquid and a conventional superfluid on the Kagome lattice using large-scale quantum Monte Carlo simulations. Our results show that the conductivity at the quantum critical point becomes a simple fraction of its value at the conventional insulator-to-superfluid transition. We explain our findings using conformal field theory. Our work opens the door for the experimental detection of anyons in a broader regime, and has ramifications for the study of quantum materials and ultra-cold atomic gases.