If his plan was to kill her by carbon monoxide poisoning (generator). Why the crazy cover up?
Yeah, and even if he thought it would be a good idea at the time, his lawyer would have told him by now, "Look, dude - we're going to go tell them that you accidentally left the thing running in the house, and that you didn't know anything about carbon monoxide. When you came back and found her, you panicked, and got rid of her body. They're going to be suspicious, and they're going to want to find the body. But you'll be in a whole lot less trouble that way than you are at the moment."