Responsa על קידושין 130:14

The betrothal of a woman in the presence of a single witness, is void. We do not require that she receive a divorce, for the mere sake of strictness, since such an act would bar her from marrying a person of priestly lineage. Nor are we apprehensive of a spreading report to the effect that the woman was betrothed, since such report would also include the information that the betrothal took place in the presence of a single witness, thus automatically nullifying the effect of the report. If it was originally reported, however, that a bona fide betrothal took place, and later it became known that the betrothal took place in the presence of a single witness, a divorce would be required, if we did not deliberately cancel false reports. Rabiah, however, ruled that we should cancel false reports.
SOURCES: Pr. 133; Mord. Kid. 537; ibid. 548; Tesh. Maim. to Nashim 2; Rashba I, 856.

Q. In the presence of witnesses Leah asked A to betroth her. While she was in a yard not owned by her, A threw a ring into her lap for the purpose of betrothal. The witnesses, although they saw Leah shake her dresses in order to brush the ring away, did not see whether or not the ring actually fell into her lap. Does Leah need a divorce from A?
A. Had the witnesses seen the ring fall into Leah's lap, she would need a divorce in spite of her claim that she never intended to become A's wife and that she was joking when she asked him to betroth her. For we would, then, be concerned only with facts and not with her thoughts and unexpressed intentions. But, since the witnesses did not see the ring fall into Leah's lap, and the yard where the incident took place did not belong to Leah, she needs no divorce, for no betrothal took place. R. Meir adds: If my teachers agree with my decision, all will be well. But if they do not agree I shall subscribe to whatever they decide to do. However, I should prefer not to be strict in this matter and not to require Leah to obtain a divorce, lest A become rebellious and refuse to divorce her, and lest he travel to a distant land and thus render it impossible for the unfortunate woman ever to marry again.
This Responsum is addressed to: "My teacher Rabbi Haim and his court."
SOURCES: Pr. 993: Mord. Git. 451; ibid. Kid. 548: Tesh. Maim. to Nashim. 1.