How does Mr. Martin present himself to Ms. Barrows on the night of his visit to her apartment?

Mr. Martin wants to lull Mrs. Burrows into a false sense of security to make it easier for him to kill her. So, instead of acting in his usually meek and mild manner, he indulges in the kind of behavior—smoking and drinking—which is likely to endear him to the similarly inclined Mrs. Burrows. But for all Martin's determination to finish Ulgine off, he doesn't have the gumption to make it happen. Despite his man-of-the-world posture he can't make that final leap to committing murder.
It's then that Mr. Martin has a brainwave. He suddenly realizes that he can achieve his goals without going to such drastic lengths as actually murdering Mrs. Burrows. However, this new plan is similar to the old one in that it involves Mr. Martin acting completely out of character. By putting on a facade of insanity he knows that not only will Mrs. Burrows be unnerved by the experience, but that she won't hesitate to inform her husband as to what happened at the earliest opportunity. And when Ulgine does so, Mr. Martin is certain that Mr. Burrows won't believe a word she says, thus undermining her credibility.

Mr. Martin at first presents himself as a modest little man not too much different from the person he appears to be at the office, except for the fact that he smokes cigarettes and drinks liquor. This is while he is still planning to murder Ulgine Barrows. She is surprised even at this difference in his personality. But while she is out of the room mixing drinks and he is looking around for something to kill her with, he has a sudden realization that he can do something much better. When she comes back with the drinks he pretends to be borderline insane. He tells her, among other things:

"I am preparing a bomb that will blow the old goat higher than hell....I'll be coked to the gills when I bump that old buzzard off."

Mrs. Barrows indignantly orders Mr. Martin to leave. She reports his behavior to their employer Mr. Fitweiler the next morning. But she ends up losing her own job because Mr. Fitweiler believe she must be insane to think that a mousy little man like Mr. Martin could have behaved the way she describes.