Nora has committed one crime, in the legal sense, and another in a moral sense. The legal infraction was forgery. The moral infraction was lying to Torvald about where she got the money to take their trip when he was ill. Each of these actions began when Nora took a loan from Krogstad.
Because Nora lied when she borrowed money from Krogstad, she must continue lying to repay the money.
Nora forged her father's signature on the loan document she gave to Krogstad. She says that her father was too ill to bother with signing the document, so she signed herself. He was actually dead when Nora forged the signature. The date on the document was what led Krogstad to his discovery.
Nora claims that this was not a crime because her father would have signed the document himself. Also, she was forging the signature for love. She wanted to save Torvald.
It is this crime, forgery, which Krogstad threatens to expose and, importantly, this is the same crime for which Krogstad lost his good reputation in town. He committed forgery too.
Nora's other transgression is her continued lie to her husband. She squirrels away money to pay off her loan to Krogstad and undertakes some sneaky methods to do this.
Nora has committed the crime of forgery.
This act of forging her dying father's name is the crux of the drama because it brings together all the underlying moral issues that contribute to the final conflict of Nora against a rigid social system in which females have little agency in their lives and marriages--a system which her husband values highly.
While Nora has committed an act that is illegal, she has responded to a higher moral principle. That is, she has valued life and love over the letter of the law. On the other hand, her husband Torvald cannot recognize the value of her act of desiring to save her husband's life over an illegality that occurred because as a woman Nora could not sign for the loan on her own. In her confrontation with Krogstad over this issue in Act I, Nora tells him that it was "impossible" for her to have disclosed to her father her purpose for the loan because he was so ill. So, after he died, she forged his name in order to save the life of her husband.
KROGSTAD. The law does not ask motives.
NORA. Then it's a bad law.... A daughter shouldn't have the right to save her husband's life? I don't know the laws very well, but I'm sure that somewhere they make allowances for cases like that.