A tensorial formalism adapted to the case of XY(3)Z symmetric tops with half integer angular momenta is proposed as an extension of the formalism for the group chain O(3) C-infinity v superset of C-3v developed in a recent paper [A. El Hilali, V. Boudon, M. Loete, J. Mol. Spectrosc. 234 (2005) 113-121]. We use the chain SU(2) circle times C-I superset of D C-infinity v(S) superset of C-3v(S), where G(S) (G being C-infinity v or C-3v) is the G point group with its spinorial representations. Coupling coefficients and formulas for the computation of matrix elements of the tensor operators are derived for this chain. A deduction of coupling coefficients (Clebsch-Gordan, 6C, 9C, ...) and similar formulas is proposed for the group C-3v(S) itself.