We demonstrate label-free molecule detection by using an integrated biosensor based on a ${\mathrm{Si}}_3{\mathrm{N}}_4∕{\mathrm{SiO}}_2$ slot-waveguide microring resonator. Bovine serum albumin (BSA) and anti-BSA molecular binding events on the sensor surface are monitored through the measurement of resonant wavelength shifts with varying biomolecule concentrations. The biosensor exhibited sensitivities of 1.8 and $3.2\mathrm{nm}∕(\mathrm{ng}∕{\mathrm{mm}}^2)$ for the detection of anti-BSA and BSA, respectively. The estimated detection limits are 28 and $16\mathrm{pg}∕{\mathrm{mm}}^2$ for anti-BSA and BSA, respectively, limited by wavelength resolution.