This is a good article that describes retrials of just penalty phase. It was written for a slightly different reason but the article talks specifically about retrials of just the penalty phase. The way I understand it is the defendent can basically try to bring in whatever they want to bring in and it will be up to the judge how much she allows and if it is admissable.
From the article, it will cover....
"there are two specific doctrinally
interesting admissibility issues: 1) to what extent may a defendant offer evidence
designed to undermine the new jurys confidence in the prior jurys verdict of
guilt; and 2) the same question with regard to the prior jurys finding of an
aggravating circumstance."
There are parts that refer to exactly what we are all wondering and well worth reading through these certain parts like this below:
"
Prosecutor Williams: Of course, the defense is not supposed to be able to make a
residual doubt argumentbut they do. For example, they cross-examine witnesses
to point out weaknesses, biasall the things they would try to do in the guilt stage
of the trial. It all depends on the judge how much of this is permitted. For
example, in one of my penalty-phase-only retrials, the judge permitted the defense
to make basically the same guilt/innocence argument it had lost at the original trial,
that is, the defendants contention that a guy named Bobby (surname unknown) did
the crime while the defendant only watched. It was very difficult for the jury to
reconcile this argument with the instructions given that they were to accept the
guilty verdict as a given. I had to argue that the defendant had presented the same
theory to the first jury, and they had rejected it."
http://moritzlaw.osu.edu/students/groups/osjcl/files/2012/05/McCord-PDF-11-29-04.pdf