The O'Connell process is a softened version (a geometric lifting with a parameter a > 0) of the noncolliding Brownian motion such that neighboring particles can change the order of positions in one dimension within the characteristic length a. This process is not determinantal. Under a special entrance law, however, Borodin and Corwin gave a Fredholm determinant expression for the expectation of an observable, which is a softening of an indicator of a particle position. We rewrite their integral kernel to a form similar to the correlation kernels of determinantal processes and show, if the number of particles is N, the rank of the matrix of the Fredholm determinant is N. Then we give a representation for the quantity by using an N-particle system of complex Brownian motions (CBMs). The complex function, which gives the determinantal expression to the weight of CBM paths, is not entire, but in the combinatorial limit a -> 0 it becomes an entire function providing conformal martingales and the CBM representation for the noncolliding Brownian motion is recovered.