We performed angular and temperature-dependent electron-spin-resonance measurements in the quasi-two-dimensional organic conductor $kappa$-(BEDT-TTF)$_2$Cu[N(CN)$_2$]I. The interlayer spin-diffusion is much weaker compared to the Cl- and Br-analogues, which are antiferromagnetic insulator and paramagnetic metal, respectively; $kappa$-(BEDT-TTF)$_2$Cu[N(CN)$_2$]I behaves insulating when cooled below $T$ = 200 K. A spin gap ($Deltaapprox$ 18 K) opens at low temperatures leading to a spin-singlet state. Due to intrinsic disorder a substantial number of spins ($sim$ 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.
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