Silicon nitride (SiN) is a promising material platform for integrating photonic components and microfluidic channels on a chip for label-free, optical biochemical sensing applications in the visible to near-infrared wavelengths. The chip-scale SiN-based optofluidic sensors can be compact due to a relatively high refractive index contrast between SiN and the fluidic medium, and low-cost due to the complementary metal-oxide-semiconductor (CMOS)-compatible fabrication process. Here, we demonstrate SiN-based integrated optofluidic biochemical sensors using a coupled-resonator optical waveguide (CROW) in the visible wavelengths. The working principle is based on imaging in the far field the out-of-plane elastic-light-scattering patterns of the CROW sensor at a fixed probe wavelength. We correlate the imaged pattern with reference patterns at the CROW eigenstates. Our sensing algorithm maps the correlation coefficients of the imaged pattern with a library of calibrated correlation coefficients to extract a minute change in the cladding refractive index. Given a calibrated CROW, our sensing mechanism in the spatial domain only requires a fixed-wavelength laser in the visible wavelengths as a light source, with the probe wavelength located within the CROW transmission band, and a silicon digital charge-coupled device (CCD) / CMOS camera for recording the light scattering patterns. This is in sharp contrast with the conventional optical microcavity-based sensing methods that impose a strict requirement of spectral alignment with a high-quality cavity resonance using a wavelength-tunable laser. Our experimental results using a SiN CROW sensor with eight coupled microrings in the 680nm wavelength reveal a cladding refractive index change of ~1.3 × 10^-4 refractive index unit (RIU), with an average sensitivity of ~281 ± 271 RIU-1 and a noise-equivalent detection limit (NEDL) of 1.8 ×10^-8 RIU ~ 1.0 ×10^-4 RIU across the CROW bandwidth of ~1 nm.