According to Bill Bryson's Made in America (p 295):
The longest credits yet - for Who Framed Roger Rabbit - lasted six
and a half minutes and saluted 763 creative artists, technicians, and
other contributors - without mentioning Kathleen Turner, the voice of
Jessica Rabbit, who opted not to be credit.
According to Disney Voice Actors: A Biographical Dictionary (p 107), she was not paid.
Not sure why she would opt for no credit, but some thoughts:
1 - Kathleen Turner recalls the film fondly in an interview with Nathan Rabin of Random Roles, which makes it seem unlikely that she had a problem with associating her name with the film.
2 - The lack of credit may have something to do with the fact that she was 9 months pregnant while doing the voice for Jessica, her daughter being born on the last day of recording. It just may have not been something she was concerned about at the time.
3 - Besides having a baby in 1987, between 1987 and 1988, she was in 4 films and a documentary. It is possible that there were contractual issues that kept her from being credited.
4 - Because she was amazed by the creative achievements of others on the film, she may not have thought her contribution that noteworthy. She didn't accept pay after all.
5 - On a list of 763 names, who would notice?
Who Framed Roger Rabbit (1988)—“Jessica Rabbit”
KT: Ooooh. Bob
Zemeckis, what an extraordinary feat, matching animation and live
film. Nobody had done that before. That was just a remarkable process.
They kept sending me tapes of how it was going along, and how they
were shooting a scene with Bob Hoskins and this sort of metal frame
that was Jessica, that would be drawn over in later stages in the
process. And then right up to when we had to start doing the breathing
of the character, because it’s one thing to do lips and face, but the
whole body is the breath, so [I had to] go in and do all the breathing
so they could finish the body, and then go back to do the face. It was
a fascinating process.
AVC: It was a technological breakthrough, but did you suspect she
would become this widespread figure of lust?
KT: [Laughs.] I’m sort of amazed. Half the photos I get autograph
requests for are Jessica. [Laughs.]
AVC: How much of you was in that character?
KT: Oh, to me, it was just fun. I was just seeing what I could do with
AVC: Do you see Jessica as another parody of the femme fatale?
KT: No. I believe she was sincerely in love with the rabbit. They had
a good marriage.
AVC: There’s that famous line, “I’m not bad, I’m just drawn that way.”
KT: Well, yes, that was just too fun to pass up.