Atomically thin 2D materials such as transition metal dichalcogenides (TMDs) provide a wide range of basic building blocks with unique properties, making them ideal for heterogeneous integration with a mature chip platform for advances in optical communication technology. The control and understanding of the precise value of the optical index of these materials, however, is challenging, as the standard metrology techniques such as the millimeter-large ellipsometry is often not usable due the small lateral 2D material flake dimension. Here, we demonstrate an approach of passive tunable coupling by integrating few layers of MoTe₂ onto a microring resonator connected to a waveguide bus. We find the TMD-to-ring circumference coverage length ratio required to precisely place the ring into a critical coupling condition to be about 10% as determined from the variation of spectral resonance visibility and loss as a function of TMD coverage. Using this TMD-ring heterostructure, we further demonstrate a semiempirical method to determine the index of a 2D material (n_MoTe2 of 4.36+0.011i) near telecommunication-relevant wavelength. The placement, control, and optical property understanding of 2D materials with integrated photonics pave the way for further studies of active 2D material-based optoelectronics and circuits.