Nonadiabatic coupling matrix elements between the 1 (2)A', 2 (2)A', and 1 (2)A " electronic states of the C2H radical are computed using ab initio full valence active space CASSCF method. The line-integral technique is then applied to study possible geometric phase effects. The results indicate the existence of a unique conical intersection due to CCH bending between the 1 (2)A' and 2 (2)A' states at the linear configuration in the vicinity of r(CC)=1.35 Angstrom and r(CH)=1.60 Angstrom. The line-integral calculations with ab initio nonadiabatic coupling terms confirm that when a path encircles the conical intersection, the line integral always produces the value pi for the topological (Berry) phase and when a path encircles the two (symmetrical) conical interactions or none of them, the line integral produces the value of zero for the topological phase.