  We report detailed measurements of the interlayer magnetoresistance of the
layered organic superconductor $\kappa -(BEDT-TTF)_2Cu(SCN)_2$ for temperatures
down to 0.5 K and fields up to 30 tesla. The upper critical field is determined
from the resistive transition for a wide range of temperatures and field
directions. For magnetic fields parallel to the layers, the upper critical
field increases approximately linearly with decreasing temperature. The upper
critical field at low temperatures is compared to the Pauli paramagnetic limit,
at which singlet superconductivity should be destroyed by the Zeeman splitting
of the electron spins. The measured value is comparable to a value for the
paramagnetic limit calculated from thermodynamic quantities but exceeds the
limit calculated from BCS theory. The angular dependence of the upper critical
field shows a cusp-like feature for fields close to the layers, consistent with
decoupled layers.
