In this work we discuss the refractive index (RI) sensitivity of a micro-cavity in-line Mach-Zehnder interferometer in the form of a cylindrical hole (40-50 μm in diameter) fabricated in a standard single-mode optical fiber using a femtosecond laser. The surface of the micro-cavity was coated with up to 400 nm aluminum oxide thin film using the atomic layer deposition method. Next, the film was progressively chemically etched and the influence on changes in the RI of liquid in the micro-cavity was determined at different stages of the experiment, i.e., at different thicknesses of the film. An effect of transition between sensitivity to the film thickness (surface) and the RI of liquid in the cavity (bulk) is demonstrated for the first time. We have found that depending on the interferometer working conditions determined by thin film properties, the device can be used for investigation of phenomena taking place at the surface, such as in case of specific label-free biosensing applications, or for small-volume RI analysis as required in analytical chemistry.