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It's from.. "Oh, the Places You'll Go!" by Dr Seuss.
When Nunally arrives and phones Crawford, he clearly identifies himself as the Hostage Negotiator. Crawford would have known this which is why he set up a supposed hostage situation.
Obviously the motel visit wasn't the first time he had spied on them, and had discovered the gun type previously.
The idea is that he did check, when she was on the floor of the living room. But then he dragged her into the library - to hide her, an essential part of the trap - and it was in the course of moving her that he undid the blockage and she was able to breathe again. This can, in fact, happen. It was in the original script, but later removed for reasons of economy.
It was a 'one-in-a-million fluke' that caused the bullet to lodge in her skull without killing her instantly. The main plot of the film rests on that fluke. If she had died then the charge would have been murder and the Double Jeopardy rule would have applied.
Ballistics tests could show that it came from the same gun that Nunally used to kill himself. Because it was the same type gun that Crawford had, it would explain how the murder weapon got out of the house. Corroborating this is the security footage showing that Crawford was at the hotel when the cop and the wife were there, so they have a plausible explanation for how Crawford switched guns the first time.
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