The recently synthesized two-dimensional metal bis(dithiolene) complex (MDT), a kind of metal-organic framework with a kagome lattice structure, has been found to be a promising material for electronic devices. Here we report the surface adsorption effects of gas molecules on the electronic properties and transport behaviors of two-dimensional MDT (M = Fe, Co, Ni, Pd, and Pt) films. The first-principles results reveal that the MDT nanosheets are selectively sensitive to different adsorbed molecules, such as CO, NO, and O2 molecules. All the studied gas molecules can be chemically adsorbed on the ferromagnetic FeDT and CoDT nanosheets, whereas the non-magnetic PdDT and PtDT films are only sensitive to NO molecules, showing quite weak interaction with CO and O2. The physisorption of CO on PdDT and PtDT originates from the mismatch of energy levels between the metal dz2 orbitals and the CO σ orbitals. In contrast, the Pd and Pt dxz and dyz orbitals can well align with the NO π* orbitals, causing strong chemisorption. More importantly, the adsorption of NO on PdDT and PtDT not only induces a magnetism of 1.0 μB for the two films but also greatly enhances the conductivity. In the case of PtDT, we observe a transition from the semiconducting to the metallic phase on NO adsorption. This significant change in the electronic structure can be understood from the adsorption-induced interfacial charge transfer and the strong orbital hybridization between the metal d states and the NO π* states. Our results suggest the potential application of the PdDT and PtDT nanosheets in gas sensing and spintronics.