We present an analytical, numerical, and experimental study of the switching time and jitter of current-induced polarization switching in vertical-cavity surface-emitting lasers (VCSELs) as an example of switching in a nonlinear system in the presence of noise. Assuming that the switching is induced by changes in the dichroism, the problem can be reduced to the first-passage-time problem in gain-switched Class-A lasers. The theoretical results show excellent agreement both with numerical simulations based on the full-rate equations model and with experiments performed on oxide-confined VCSELs.