He kills Dick and goes to the intercom and says "Dick Laurent is dead" presumably to inform his wife. But then the cops chase him. He was supposed to have killed his wife afterwards. If he did so then why leave that message?
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Good interpretation.
shareI'm not convinced that he did. My take on it is that at the beginning of the film his subconscious is trying to remind him that he killed Laurent, his conscious mind trying to block that fact out. Everything that unfolds afterwards is his mind trying to reconcile events as they actually happened with events the way he remembers them.
While playing at the club he remembers seeing Renee leave with Andy from a previous night, and begins to play frantically as he panics a little. On the night he's seeing a flash of he followed them to the Lost Highway Hotel where he found Renee with Laurent, he waits for her to leave and then kills Laurent. This was probably, at most, a few days before the film begins.
I think that someone saw him take Dick away - represented in Fred's head as the Mystery Man, who I think is filling in for someone that Fred doesn't know/never saw every time he appears. And that person begins to mock him by sending him tapes/threats. That person likely kills Renee and Fred finds the aftermath, at this point his mind is threatening to break and he genuinely can't remember if he killed her (though he knows, on some level, that he was responsible for her death either way).