We performed angular and temperature-dependent electron-spin-resonance measurements in the quasi-two-dimensional organic conductor κ -(BEDT-TTF)2Cu [ N (CN) 2] I . The interlayer spin diffusion is much weaker compared to the Cl and Br analogs, which are antiferromagnetic insulator and paramagnetic metal, respectively; κ -(BEDT-TTF)2Cu [ N (CN) 2] I behaves insulating when cooled below T =200 K . A spin gap (Δ ≈18 K ) opens at low temperatures leading to a spin-singlet state. Due to intrinsic disorder a substantial number of spins (∼1 % ) remains unpaired. We observe additional signals below T =4 K with a pronounced anisotropy indicating the presence of local magnetic moments coupled to some fraction of those unpaired spins.