I would say that the climax to the plot does not come until after Mr. Fitweiler has called Mr. Martin into his office and questioned him about what he did the night before. Mr. Fitweiler appears quite satisfied with Mr. Martin's story that he spent a very quiet evening, as usual, and went to bed early.
Before Mr. Martin can leave the office, Ulgine Barrows bursts in and screams, "Is the little rat denying it?" She must have realized that the story she had previously told her boss may have sounded preposterous and that she has no proof to back up a word of it. After repeating what she had previously told Mr. Fitweiler, she asks him:
"Can't you see how he has tricked us, you old fool? Can't you see his little game?"
By calling Mr. Fitweiler an old fool, she has cut her own throat. She has not only been extremely disrespectful, but she has shown her true opinion of her employer. This is the climax. Mr. Martin has achieved his goal of making her look crazy and has won the victory in the conflict that is the essence of the plot.
I would say that it is when Martin arrives at Mrs. Barrows home and comes up with his new plan (rather than the murder he'd intended) to rid himself and his company of the annoying woman. (He's angry because she has destroyed what Martin considers to be a highly efficient system of organization at their company.)
Martin then tells the incredulous Mrs. Barrows that he is going to "blow up" the company president but only when he is good and high on heroin. He knows he is "sitting in the catbird seat" because no one will ever believe her accusations. He has been too much of a "model employee" for that.
It is a perfect plan. Mr. Fitzwater believes Mrs. Barrows has suffered a nervous breakdown and dismisses her from employment.