The scalar top quark can be the lightest charged supersymmetric particle and it can be lighter than the top quark itself in supersymmetric extensions of the Standard Model. A search for a scalar top quark has been performed using a total data sample of 15.2 pb - 1 at centre-of-mass energies of s = 130, 136, and 161 GeV collected with the OPAL detector at LEP. No evidence was found above the background level expected from the Standard Model. The 95% C.L. lower limit on the scalar top quark mass is 58.7 GeV, if the mixing angle between the supersymmetric partners of the left- and right-handed states of the top quark is smaller than π/4. If the mixing angle is zero, the limit is 65.4 GeV. These limits were obtained on the condition that the scalar top quark decays into a charm quark and the lightest neutralino, and that the mass difference between the scalar top quark and the lightest neutralino is larger than 10 GeV. Assuming a relatively light scalar neutrino, we also studied the complementary decay mode of the scalar top quark in which it decays into a bottom quark, a charged lepton, and a scalar neutrino. A mass limit on the light scalar bottom quark was also set in this study.