1,835. A Man and a Woman Who Disagree as to Whether or Not They're Divorced

Hilchos Geirushin 12:3

Let’s say that the woman’s husband objects that he never gave her the get. Rather, he claims that he lost it and she found it. In such a case, his words are not accepted. This is because he concedes that he wrote it for her, and it’s now in her possession. However, if he says that he gave the get to her conditionally, or for safekeeping, or that he never wrote it and it’s a forgery, then the woman must have the signatures on the get validated or the witnesses to its delivery testify. If the signatures are not validated, she is not considered divorced when it comes to marrying others but she is disqualified from marrying a kohein, as we stated earlier (halacha 12:1). She brought that ramification about through her own statements.

Hilchos Geirushin 12:4

If a woman comes with her husband and says, “My husband divorced me but I lost the get,” and he says, “I didn’t divorce her,” her word is accepted even if there’s a presumption that she’s his wife. This is because we assume that a woman wouldn’t make such a bold lie in front of her husband.