$H_2S$ micro-gas sensors have been developed employing $SnO_2$:CuO composite thin films. The films were prepared by e-beam evaporation of Sn and Cu metals on silicon substrates, followed by oxidation at high temperatures. Results of various studies, such as scanning electron microscopy (SEM), X-ray diffraction (XRD) and X-ray photoelectron spectroscopy (XPS) reveal that $SnO_2$ and CuO are mutually non-reactive. The CuO grains, which in turn reside in the inter-granular regions of $SnO_2$, inhibit grain growth of $SnO_2$ as well as forming a network of p-n junctions. The film showed more than a 90% relative resistance change when exposed to $H_2S$ gas at 1 ppm in air at an operating temperature of $350^{circ}C$ and had a short response time of 8 sec.