This technical note addresses the existence of a common linear copositive Lyapunov function (CLCLF) for continuous-time switched positive linear systems. Two necessary and sufficient conditions for the existence of a CLCLF are provided. One condition shows that the existence of a CLCLF for a family of n x n-dimensional Metzler matrices can only be determined by n - 1 lower dimensional Hurwitz matrices. The other condition further shows that the existence of a CLCLF is also determined by n - 1 characteristic constants, which gives an easily verifiable computation algorithm without checking a large amount of Metzler Hurwitz matrices.