In a 1997 essay, W. L. Petersen argued for a literary connection between the Pericope adulterae (= PA) and the Protoevangelium of James on the basis of the common phrase “neither do I condemn you” (ουδε εγω σε [κατακρινω]).  While in the PA Jesus utters these words to the accused woman (John 8:11), in the Protoevangelium the high priest pronounces them over Mary and Joseph, declaring them innocent of the charge that Mary’s virginity has been compromised.
Petersen assumed that the Protoevangelium must depend on an earlier form of the PA tradition without so much as mentioning the possibility that the PA, if it were a late tradition, might in fact depend on the Protoevangelium. As we might expect, Petersen’s essay is typically cited in discussions of the PA as a second-century tradition. But if we regard the PA in its fullest form as a fourth-century development, there is no reason the dependency must go in this direction. In fact, if we regard this saying as one of the final features of the PA, the only possible connection (if we accept a connection) is from the PA to the Protoevangelium. But if such a connection is plausible, we have a potentially valuable clue as to the interests of the fourth-century compilers of the PA in the antidicomarianite and related controversies concerning the virginity of Mary.
 “ΟΥΔΕ ΕΓΩ ΣΕ [ΚΑΤΑ]ΚΡΙΝΩ, John 8:11, The Protevangilum Iacobi, and the History of the Pericope adulterae” in Sayings of Jesus: Canonical and Non-canonical (ed. W. L. Petersen, J. S. Vos, and Henk J. de Jonge; Leiden: Brill, 1997), 191-221.