The defense attorney suggested that Basham failed a lie-detector test, while Fulks, who has given three consistent statements laying most of the blame on Basham, passed.
Blume also asked for separate trials because, he said, each of the men's statements to police could unfairly implicate the other.
Prosecutors have offered to cross-out portions of each man's statements that accuse the other. But Blume said that would leave a jury thinking that the suspect giving the statement was solely involved with everything.
"A prosecutor seeking two death sentences could hardly want more but is entitled to much less," Blume wrote.
Prosecutors and Basham's lawyers have not filed a response to the motion.
Filings show Basham may be considering an insanity defense. The deadline for that decision comes later this year.
The trial is scheduled to start April 5.
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