Series expansions have been derived for the percolation probability of a generalized Domany - Kinzel cellular automaton with two equivalent absorbing states. The analysis of the series generally yields estimates of the critical exponent , consistent with earlier Monte Carlo studies thus confirming that the model belongs to the same universality class as branching annihilating random walks with an even number of offspring. There is evidence to suggest that when the probability of spreading from two active sites becomes small a new critical behaviour emerges.