Excitation energies and mean lives of levels in $^{38}\mathrm{K}$ up to 3.85 MeV, excited in the $^{40}\mathrm{Ca}(d,\ensuremath{\alpha}\ensuremath{\gamma})^{38}\mathrm{K}$ reaction at ${E}_{d}=4.421$ MeV, have been measured using the Doppler-shift attenuation method. The $\ensuremath{\gamma}$ rays were detected at 31.7 and 121.7\ifmmode^\circ\else\textdegree\fi{} in coincidence with $\ensuremath{\alpha}$ particles detected in an annular detector with an average angle of 169\ifmmode^\circ\else\textdegree\fi{}. The following mean lifetimes were found (excitation energy in keV, lifetimes in fsec): 459, g 4000; 1698, 65 \ifmmode\pm\else\textpm\fi{} 17; 2401, 90 \ifmmode\pm\else\textpm\fi{} 25; 2613, ${9000}_{\ensuremath{-}2000}^{+7000}$; 2646, g 12000; 2829, 280 \ifmmode\pm\else\textpm\fi{} 70; 2870, 4500 \ifmmode\pm\else\textpm\fi{} 1200; 2993, 220 \ifmmode\pm\else\textpm\fi{} 50; 3315, 2450 \ifmmode\pm\else\textpm\fi{} 420; 3342, 55; 3668, 150; 3725, 120; 3849, 55. Several spin-parity restrictions made in earlier work have been made stricter on the basis of these results.